The Sky Bet EFL League One side's quality showed, despite a valiant performance from the Non League side.
Town dominated proceedings and nearly broke the deadlock after just 3 minutes, a right wing cross picked out Conor Chaplin free from six yards out whose header was glanced just wide of the top near.
The first shot on target then followed two minutes later, the ball fell to Conor Chaplin on the right-hand edge of the box, whose low fierce strike was creeping into the bottom near corner, forcing a good diving save from goalkeeper Theo Richardson who held onto the effort well.
Buxton up other end did test Christian Walton two minutes later, albeit a comfortable save for the Town number 1, with the low shot from the edge at the box hit straight at the goalkeeper to catch.
While Wes Burns' cross driven across the box was punched away by goalkeeper Theo Richardson in the 9th minute, Gassan Ahadme's header from point blank range, following Leif Davis' great left wing corner, went just wide of the top near corner three minutes later.
Chances continued to fall for Town, Burns again whipped in a dangerous right wing cross into the danger area, only this time Richardson was alert on his line to claim the ball well with Town players arriving from point blank range on 14 minutes, while the winger's powerful cross-shot from distance out on the right wing went straight into Richardson's chest soon after.
Davis' left wing cross then picked out Conor Chaplin free from close range on 17 minutes, but the attacking midfielder's effort was deflected wide into the bottom near side-netting for an Ipswich corner. Chaplin turned provider a minute later though, the latter was fed through on the left hand side of the box to lift a great ball across, which was glanced onto the unmarked Ahadme but his close range header went straight to Richardson.
Chaplin, who was by far the Man Of The Match, then drew a good stop from Richardson on 22 minutes, the Town number 10's dangerous 30-yard free-kick took a deflection off the wall towards the bottom near corner, which Richardson did well to recover and pounce on the ball after initially spilling it.
Had it not been for the woodwork, Town would've taken the lead just after the half-hour mark, after Richard Keogh's strike following a left wing corner was blocked, the ball fell to Cameron Humphreys on the left-hand edge of the box whose fierce strike went just over, via a deflection off the top of the crossbar.
With two goals in the space of five minutes, Town quickly took advantage of the 3 leagues difference. Wes Burns capped a brilliant surfing run with a great low cross into the box from the right wing, finding Conor Chaplin from 8-yards out who took a good touch to control it before unleashing a smart powerful left footed strike into the bottom right hand corner for his seventh goal of the campaign, and first in any cup competition, as well as his 18th goal of his Town career, 1-0 Ipswich after 33 minutes.
It was soon 2-0 to the Blues, captain Sam Morsy threaded a great ball to find goalscorer Chaplin, he in turn found Kyle Edwards on the spin, the latter cleverly beat his defender before lifting a great ball across the six yard box for Gassan Ahadme to turn home his maiden Town goal, on the slide into the empty net from 3-yards out.
Three minutes later, Conor Chaplin could only direct his close range diving header wide of the near post from Edwards' brilliant left wing cross, a minute prior to Wes Burns' ball smashed across the six yard box being parried away by the diving Richardson at his near post, where a Buxton defender duly smacked the ball behind for a corner which saw a free header towards the roof of the net crucially cleared off the line.
Town then looked to test Richardson on 45 minutes, but the free header from another great left wing delivery was headed straight at the Bucks' shot-stopper.
Town started the second half though displaying the same attacking intent as the first half, substitute Tawanda Chirewa was quick to twat Richardson just five minutes after the restart. The youngster was fed into space on the edge of the box to smash a great shot across goal towards the bottom right hand corner, forcing Richardson to smartly dive down and beat the ball away.
Ahadme meanwhile saw a great glancing header at the far post denied by the face of the left-hand post from Burns' audacious right wing cross five minutes later, while Kyle Edwards' close range bicycle kick went over the bar from substitute Luke Woolfenden's right wing ball on 62 minutes.
Seven minutes later, another Town substitute Kayden Jackson went close to extending Town's lead, the forward just unable to connect with a great left wing ball across from six yards out.
But with the goal of the night and arguably one of the best of the competition, Conor Chaplin stole the headlines with a beautiful finish in the 73rd minute. Alfie Armin leapt highest to nod the ball onto the midfielder in space on the left-hand edge of the box, who rifled a rocket of a strike into the top far corner for his second goal of the evening, 3-0 Ipswich.
A vital goal-line clearance from Albie Armin however preserved Town's clean sheet with Buxton's best opportunity of the game on 76 minutes, Max Conway - making his debut on-loan from Bolton Wanderers - broke into the box down the left-hand side, drawing Walton off his line in the process although the shot at goal was crucially cleared just ahead of the goal-line by Armin with Walton off his line. The rebound though fell to Harry Bunn whose shot was deflected just wide of the bottom near left hand corner for the visitors'first corner of the night, which saw a shot at the far post blocked.
After Kieran McKenna handed a First Team debut to Matt Ward late on, an insane one handed catch from Richardson denied Town a fourth goal after 86 minutes. Kyle Edwards broke onto the left-hand byline in acres of space to lift a great ball across to Chaplin at the far post, the latter leapt highest to head the ball across goal only to be denied a hat-trick by the outstretched right arm of Richardson to brilliantly hold onto the ball.
Town however did wrap up proceedings with a fourth goal in the second minute of stoppage time, Kayden Jackson picked the pocket of a Buxton player midway through the away side's half before driving onto the edge of the box to slam home his third goal of the season and 24th for the club into the bottom left hand corner.
A valiant effort from Buxton however sees their FA Cup run draw to a close, while Ipswich progress to the Third Round Proper for the first time in four season with the reward a home tie against familiar opponents Rotherham United, who are now in the Sky Bet EFL Championship, most likely to be played on Saturday 7th January 2023 at Portman Road.
Ipswich Town:-
1 Christian Walton
24 Kane Vincent-Young
2 Richard Keogh
15 Cameron Burgess
3 Leif Davis (HT' Armin)
5 Sam Morsy (c) (59' Woolfenden)
30 Cameron Humphreys (HT' Chirewa)
7 Wes Burns (59' Jackson)
10 Conor Chaplin
29 Kyle Edwards
18 Gassan Ahadme (82' Ward)
Subs:
31 Vaclav Hladky
4 George Edmundson
6 Luke Woolfenden
39 Edwin Agbaje
36 Alfie Armin
38 Xander Siziba
42 Tawanda Chirewa
41 Matt Ward
19 Kayden Jackson
Buxton:-
1 Theo Richardson
12 Declan Poole
16 Shaun Brisley
4 Jake Moult
18 Sean Newton (C)
3 Max Conway (77' Sargent)
21 Sam Osborne
8 Connor Kirby
6 Lindon Meikle (83' Gilchrist)
10 Tom Elliott (60' Bunn)
19 Jack McKay (61' Boden)
Subs:
13 Matthew Hudson (GK)
5 Josh Granite
9 Diego De Girolamo
14 Jason Gilchrist
20 Serhat Tasdemir
23 Harry Bunn
25 Scott Boden
26 Oliver Sherwood
29 Matt Sargent
Booked: Brisley (23'), Davis (27'), McKay (28'), Chirewa (49'), Morsy (55').
Attendance: 9,817
Goals: Chaplin (33', 73'), Ahadme (38'), Jackson (90'+2').
