Diego Costa confirmed his status as the club’s number one striker with his 20th league goal of the season, a 36th minute penalty to cancel out Steven Fletcher’s opening goal before Loic Remy completed the win with two second half goals.
Didier Drogba, meanwhile, was carried from the field by his team-mates when he was replaced after a brief, 28-minute appearance that had all the signs of a final farewell.
Mourinho and his staff lined up on the touchline to applaud the 37-year-old as he left the field saluting to the crowd.
The forward is out of contract this summer and it was clear from his reaction that his second spell at the club is now coming to a close.
Meanwhile, Hull City were relegated after drawing 0-0 at home to Manchester United.
Hull needed to defeat United to stand any chance of staying up, but their failure to do so left them three points adrift of safety.
The visitors, missing injured goalkeeper David de Gea and on-loan striker Radamel Falcao, lost Angel di Maria to injury and saw substitute Marouane Fellaini sent off for an ugly foul on McShane in the second half.
But Steve Bruce was unable to engineer a first managerial win over his old employers as Hull sank into the Championship and Louis van Gaal's United finished the campaign in fourth place.
Newcastle United were the only other team at risk of relegation, but they secured their top-flight status with a 2-0 victory at home to West Ham United.
Jonas Gutierrez, who returned to action last month after a 17-month battle with testicular cancer, was Newcastle's saviour, teeing up Moussa Sissoko for a 54th-minute header and scoring with a deflected effort.
Newcastle owner Mike Ashley, criticised by fans for a perceived lack of investment, had vowed prior to the game not to leave until the club win a trophy or qualify for the Champions League.
West Ham, meanwhile, announced after the match that manager Sam Allardyce's contract will not be renewed and he will leave the club with immediate effect.
Liverpool captain Steven Gerrard scored in vain on a wretched 710th and final appearance for the club as Brendan Rodgers's side capitulated in a humiliating 6-1 defeat at Stoke City.
With Raheem Sterling benched over his contract stand-off, Liverpool conceded five first-half goals, with Mame Biram Diouf scoring twice and Jonathan Walters, Charlie Adam and Steven Nzonzi also on target.
Gerrard replied in the second half, to give the visiting fans one last goal before his departure for the Los Angeles Galaxy, but ex-Liverpool striker Peter Crouch restored Stoke's five-goal cushion late on.
Liverpool's sixth-place finish nevertheless takes them into the Europa League, alongside Tottenham Hotspur, who won 1-0 at Everton courtesy of Harry Kane's 21st goal of the league campaign and 31st in all competitions.
Gerrard's former England team-mate Frank Lampard also found the net in his final game before leaving England for the United States, but he scored in a winning cause as runners-up Manchester City beat Southampton 2-0.
The 36-year-old midfielder converted a cross from James Milner in the first half at the Etihad Stadium, with Golden Boot-winner Sergio Aguero scoring his 26th goal of the campaign late on.
Arsenal rubber-stamped third place, and automatic Champions League qualification, by demolishing West Bromwich Albion 4-1 as Theo Walcott staked a claim for a cup final starting place with a first-half hat-trick.
Jack Wilshere was also on target, with Gareth McAuley replying for West Brom.
Aston Villa will go into the FA Cup final on the back of a defeat after a first-half Danny Ings header saw them beaten 1-0 at relegated Burnley.
Leicester City celebrated their stunning escape from relegation with a 5-1 romp at home to relegated Queens Park Rangers.
In the day's other game, Crystal Palace beat Swansea City 1-0 courtesy of a 57th-minute goal by Marouane Chamakh.
Palace, who picked up their ninth victory since former Newcastle handler Alan Pardew took over in January, took their points tally to 48 and a 10th place finish.