Chelsea were bidding to take over from Liverpool at the summit, but their loss to the league's bottom club means that Brendan Rodgers's side can now open up a five-point lead if they win at Norwich City on Sunday.
Samuel Eto'o put Chelsea ahead after only 12 minutes, but Sunderland equalised quickly through Connor Wickham and claimed victory thanks to an 82nd-minute penalty from on-loan Liverpool striker Fabio Borini.
Mourinho, who had avoided defeat in his previous 77 home league games as Chelsea manager, hit out sarcastically at referee Mike Dean after the game.
"I just want to say four things, and I'm sorry, because if you make me (answer) more questions, I will repeat in exactly the same way," he told Sky Sports.
"Congratulations to my players, because they gave what they have and what they don't have. Congratulations to Sunderland, because they won. Congratulations to Mike Dean, because he made a fantastic performance.
"And congratulations to Mike Riley (head of refereeing body Professional Game Match Officials Limited), because what they did during the season was fantastic for the way the championship is going."
He was referring to the 81st minute, when Cesar Azpilicueta was penalised for sliding in on Jozy Altidore and Borini, a former Chelsea striker, calmly beat Schwarzer from the spot to win the match.
The penalty incident saw Altidore fall after bringing his standing foot down on Azpilicueta's leg and Chelsea reacted furiously, with assistant coach Rui Faria needing to be restrained as he berated Dean.
Having held third-placed Manchester City to a 2-2 draw in midweek, Sunderland have emerged as this season's kingmakers, and victory at Stamford Bridge gave their chances of avoiding relegation a sizeable boost.
Gus Poyet's side, who had previously gone nine games without a win, finished the day three points from safety and also have a game in hand to play.
"As soon as I said we needed a miracle, things changed," said Sunderland manager Poyet, a former Chelsea player.
"The players kept believing. We needed something special and it happened in the last four or five days, but it is not over for us yet."
Chelsea took the lead in the 12th minute, Eto'o volleying in from Willian's left-wing corner, but it took Sunderland only six minutes to draw level.
Mark Schwarzer, deputising in goal for Chelsea in place of the unwell Petr Cech, spilled a long-range shot from Marcos Alonso and Wickham -- who claimed a brace at City -- pounced to clip home the rebound.
Chelsea's response was not slow in coming and visiting goalkeeper Vito Mannone had to produce smart saves to thwart Branislav Ivanovic, Nemanja Matic, Mohamed Salah and Willian before half-time.
Chelsea's frustrations told when Ramires lashed out at Sebastian Larsson with his arm, catching the Sunderland midfielder in the face, but Dean appeared not to see the incident.
The Chelsea onslaught continued in the second half, with Eto'o curling just wide and substitute Demba Ba miscuing from Willian's cut-back, but the goal would not come and there was worse to follow.
Then came The Penalty, as they are calling it today.
Earlier, Fulham squandered an opportunity to escape from the Premier League relegation zone after going down 3-1 at London rivals Tottenham Hotspur.
Fulham equalised almost immediately through Steve Sidwell after Paulinho put Tottenham ahead in the 35th minute, but second-half goals from Harry Kane and Younes Kaboul saw the hosts prevail.
"If we had got any points here, it would have been an extra point for us," said Fulham manager Magath, whose side ended the day two points from safety.
"We have to win our home games and I think we can manage it."
Fulham slipped one place to 19th after Cardiff City moved above them on goal difference by drawing 1-1 at home to Stoke City.
Marko Arnautovic gave Stoke the lead from the penalty spot in first-half injury time, but Peter Whittingham earned Cardiff a draw with a penalty of his own after Steven Nzonzi tripped Fraizer Campbell.
Elsewhere, an ice-cool stoppage-time penalty by Wilfried Bony gave Swansea City a 2-1 victory at Newcastle United that took the Welsh club six points clear of the relegation zone.
Aston Villa spurned a chance to put clear daylight between themselves and the bottom three in a 0-0 draw at home to Southampton, while a 59th-minute Mile Jedinak penalty saw Crystal Palace win 1-0 at West Ham United.