Sunderland, who secured survival with a point at Arsenal during the week, held the home side deep into the second period, but Loic Remy scored twice in the final 20 minutes to secure all the points for the capital outfit.

Chelsea started on the front foot and came close to taking the lead in the fourth minute when Didier Drogba met a cross from Juan Cuadrado, but the honorary Blues skipper could not find the back of the net.

The visitors came close to breaking the deadlock in the 13th minute when Sebastian Larsson tried his luck with a 25-yard free kick, but his dipping effort was pushed away by Petr Cech on what could be his final appearance in a Chelsea shirt.

Branislav Ivanovic then came close for the home side down the other end, but Vito Mannone was alert to make a smart save.

Sunderland's English-born Scottish striker Steven Fletcher scores during the English Premier League football match between Chelsea and Sunderland at Stamford Bridge in London on May 24, 2015 © Getty Images

It was Sunderland that took the lead, however, with Steven Fletcher heading a deep Adam Johnson corner home at the back post in the 25th minute.

Chelsea were then forced to substitute Drogba on what was his final appearance in a Blues shirt, with the Ivorian leaving the field for Diego Costa.

The hosts were awarded a penalty in the 35th minute when John O'Shea felled Cuadrado, and Costa stepped up to finish into the corner and level the scores with his 20th league goal of the season.

Chelsea's Ivorian striker Didier Drogba is carried off the pitch by teammates after being substituted during the English Premier League football match between Chelsea and Sunderland at Stamford Bridge in London on May 24, 2015 © Getty Images

The home side had the first real chance of the second period in the 50th minute when Costa set up Remy inside the box, but the Frenchman could only place his effort wide of the post.

Sunderland remained a threat, however, and came close just before the hour when Patrick Van Aanholt fired a shot towards the bottom corner, but Cesar Azpilicueta managed to clear off the line.

Chelsea's next chance arrived when Gary Cahill collected a pass from Eden Hazard inside the box, but the defender's effort was straight at Mannone.

The Premier League champions did take the lead with 20 minutes remaining as Hazard set up Remy to finish into the bottom corner.

Sunderland had the chance to level moments later when Van Aanholt found Fletcher, but the Scot could only head wide of the post. Down the other end, Mannone made a smart stop to deny Willian as the game flowed from end to end.

Chelsea added a third late on through Remy as the champions rounded off their season with all three points.