Diego Costa, a first-half substitute for Drogba, scored from the spot to cancel out Steven Fletcher’s opener before Loic Remy came off the bench to score twice in the last 20 minutes of the match.
With Sunderland having secured their Premier League status in midweek at Arsenal and Chelsea having long since wrapped up the title, there was a jovial mood at Stamford Bridge on the day they lifted the trophy.
For Drogba, in particular, it was an emotional exit having announced that this would be his final appearance for the club and he was given the full treatment by the Chelsea faithful.
The Ivorian was made captain for the day before being substituted after just half an hour with his team-mates chairlifting him off the field to a huge ovation from Roman Abramovich among others.
Jose Mourinho was rather more reserved given that Chelsea were already a goal down at that point with Fletcher having headed home unmarked from Adam Johnson’s corner.
The scenes that greeted Drogba’s withdrawal might have suggested that Chelsea minds were elsewhere but they were soon level through his replacement Costa.
John O’Shea was adjudged to have fouled Juan Cuadrado and Costa stepped up to take the resultant spot-kick, beating Vito Mannone from 12 yards for his 20th Premier League goal of the season.
Sunderland won at Stamford Bridge last season and they remain the only team to have beaten Mourinho’s Chelsea on their own turf in the Premier League.
The visitors certainly had their moments on Sunday too with Petr Cech, another who could be set to leave Chelsea in the summer, being forced into smart saves from Seb Larsson and Jermain Defoe.
Chelsea played some entertaining football after the break as they probed for a winner but Sunderland remained a threat at the other end with the champions uncharacteristically open.
When the impressive Patrick van Aanholt found space once more on the left flank, Cech could only parry his cross into the path of Defoe and his shot was cleared near the line by Cesar Azpilicueta.
Sunderland, who finish 16th, were punished soon afterwards when Eden Hazard fed Remy in a central position and the French forward fired in a low shot that Vito Mannone could only palm into the net.
Mannone did rather better to keep Sunderland in the game and deny Willian when the Chelsea man headed low towards the near corner.
But he could do nothing to prevent Remy having the final say with a neat near-post finish from Nemanja Matic’s low left-wing cross bringing his seventh of the season and second of the afternoon.
The final whistle followed soon after with John Terry leading the celebrations on the day he became the first man since Gary Pallister to play every minute of a Premier League title-winning campaign.
The victory also means Chelsea finish the season on 87 points – their best total since their last Premier League title victory under Mourinho in 2006 – and an eight-point lead over Manchester City in second spot.
Chelsea: Cech (7), Ivanovic (6), Cahill (6), Terry (6), Azpilicueta (6), Mikel (6), Matic (7), Cuadrado (6), Willian (7), Hazard (7), Drogba (6).
Subs used: Costa (7), Remy (8), Christensen (6).
Sunderland: Mannone (6), Jones (6), Coates (6), O’Shea (5), Van Aanholt (7), Johnson (6), Larsson (6), Rodwell (6), Wickham (6), Defoe (7), Fletcher (7).
Subs used: Giaccherini (6).
Man of the match: Loic Remy