Wimbledon’s second came through captain, Will Nightingale, who met a Jack Rudoni free-kick to head home the second.
Ayoub Assal, who caused the Swindon defence a serious headache all game, scored the Dons' third goal by tapping home Ollie Palmer's deflected shot.
Pigott added a fourth early into the second half, turning home a Assal cross to sentence Swindon to another defeat.
Tyler Smith pulled one back for the Robins with just over 10 minutes remaining. However, it was too little, too late for the away side to get back into the game.
After recording his first back-to-back win as manager of The Dons on Tuesday evening, Mark Robinson made one change to the side that put Ipswich Town to the sword, with Ben Heneghan replacing Paul Kalambayi in the heart of defence.
Rooted to the bottom of the table come kick-off, John Sheridan made several changes to the side that lost 3-0 to promotion chasers, Peterborough United, last time out.
One of those changes, Brett Pitman, came closest in the early stages, crashing a header against the post.
There could have been nerves coursing through the veins of the Wimbledon players prior to kick-off - with Wigan Athletic and Rochdale picking up wins in the relegation fight - however, the Dons’ early pressure shook off any unwanted distractions.
Ayoub Assal and Will Nightingale came close to opening the scoring, both having the ball cleared off the face of goal.
Luke O’Neil deployed on the right has become one of the key fundamentals of the Dons’ resurgence in League One. His pinpoint crosses were the key to winning against Ipswich, and Swindon were experiencing the same troubles as the Tractor Boys on Saturday.
The onslaught continued with Joe Pigott latching onto a Nesta Guinness-Walker cross, but his shot could only find the gloves of Lee Camp.
The intense pressure would finally break the Robins’ resilience on the 18th minute when Jack Rudoni was scythed down by Jonathan Grounds; handing Pigott the opportunity from the spot to open the scoring.
The 27-year-old personified coolness to slot home his 16th of the campaign and give Mark Robinson’s side the lead.
The Dons soon doubled their lead just six minutes later, when Will Nightingale, who scored in midweek, headed home a Jack Rudoni cross to give the home side extra breathing room.
Ayoub Assal had a glorious opportunity to add a third on the 38th minute, but after rounding Lee Camp, Assal could only fire his shot against the bar.
Despite being dormant for the majority of the scintillating first half, Nik Tzanev pulled out two remarkable saves to thwart Jordan Garrick from point-blank range.
But Swindon would surrender the third goal on the stroke of half-time, when Assal atoned for his earlier miss and bundled home his fourth of the season.
After nice work down the left from Jack Rudoni, he cut inside and fed Ollie Palmer. The towering forward took one touch, before unleashing a shot which fell into the path of Assal. The 19-year-old had the simple task of tapping home the third and shocking Swindon into submission.
Wimbledon came out for the second half even more fired up.
The game was well and truly finished on the 53rd minute, when Assal turned provider of Pigott, who curled a right-footed shot past the motionless Camp.
The swashbuckling football was in full swing.
Swindon’s effortless attempts to get back into the game looked like a side who are bound for relegation.
Despite Tyler Smith pulling one back for the Robins, their late assault was too little, too late.
Mark Robinson's side saw the game out with a professional, cut-throat ruthlessness.
The Dons moved five points clear of the bottom four, with the club's League One status firmly in their own hands.
As for John Sheridan's side, League Two beckons. The Robins were out-worked, out-classed and out-played by the Dons at Plough Lane.