The 35-year-old was handed the reins on a permanent basis on Wednesday, having served as head coach since Michael Laudrup was relieved of his duties in February.
And, after picking up an impressive 2-1 win at Newcastle United in their last away fixture, Swansea made another fruitful trip to the north east – Nathan Dyer putting the visitors in front in the seventh minute on the final day of the Premier League season.
Marvin Emnes doubled the advantage seven minutes later, but Fabio Borini pulled Sunderland back into the game early in the second half.
The Wearsiders' joy was shortlived, however, as Wilfried Bony re-established the two-goal lead four minutes later to wrap up the points.
Both of these sides were already assured of their Premier League safety, but the result brought to an end to Sunderland's five-game unbeaten run.
Monk used the season-closing fixture to utilise several of the club's fringe players, with youngster Jay Fulton making his full debut, while Liam Bridcutt and Phil Bardsley replaced Lee Cattermole and Marcos Alonso for Sunderland.
And it was the supposedly weakened visitors who took the lead early on – Dyer applying a wonderful chipped finish after being played in by a precise pass from Wayne Routledge.
Swansea were doing all the early pressing and were two up soon afterwards, as Emnes turned superbly on the edge of the penalty area before smashing a left-footed effort beyond Sunderland goalkeeper Vito Mannone.
There was no sign of either side taking their foot off the gas as the season neared its conclusion, making for an entertaining and open encounter at the Stadium of Light.
Sunderland began to enjoy more possession in the opposition half and went close to reducing the deficit in the 27th minute, when Sebastian Larsson's dangerous cross was inadvertently headed onto the right-hand post by Swansea defender Jordi Amat.
Bardsley, whose future remains in doubt with his contract set to expire at the end of the season, then fired an effort narrowly over the crossbar shortly before the break.
Gus Poyet's men got off the mark five minutes into the second half, when former Swansea loanee Borini beat visiting goalkeeper Gerhard Tremmel at his near post with a powerful header from Adam Johnson's corner.
But Swansea soon had their two-goal cushion restored, as Bony fired in a shot off the left-hand post from the edge of the penalty area for his 25th goal of the season in all competitions.
Larsson and Johnson’s failure to find the target with subsequent efforts did little to dampen the mood of the home supporters, who were busy celebrating the club's 'Great Escape' from relegation, with Sunderland having been bottom of the Premier League at Christmas.
