Bergwijn, a £25million signing from PSV Eindhoven this week, made an immediate impact as he opened the scoring in fine style, with Son Heung-min clinching the most impressive three points of Mourinho's reign in north London so far.
City, who were reduced to 10 men when Oleksandr Zinchenko saw red, missed a first-half penalty through Ilkay Gundogan while Sergio Aguero also hit a post as they failed to score for the first time in 24 away games.
Raheem Sterling was lucky to avoid a red card on a bad afternoon which saw City suffer a sixth defeat of the season, edging Liverpool even closer to the title.
For Spurs, this could do wonders for their top-four hopes as they are four points behind Chelsea and will hope to kick on from here.
It was a classic encounter between two heavyweights, filled with drama from the off.
The first moment of controversy came in the 12th minute when Sterling managed to swerve being dismissed.
With 11 men on the pitch, City assumed control and, through Riyad Mahrez down the left, looked dangerous.
Mahrez was involved as they almost took the lead in the 27th minute as he latched on to a loose pass by Davinson Sanchez and played in Aguero, who looked destined to score, only for Hugo Lloris to somehow turn his shot onto a post with an outstretched foot.
That was only just the beginning of the drama though as VAR and, predictably, Dean came to the forefront in the build-up to half-time.
First City were awarded a penalty after Serge Aurier went through the back of Aguero. Dean did not award it at the time, but after play finally stopped over two minutes later after VAR had ruled it a foul.
Mourinho was seen laughing in the dugout, though there was more to come.
Lloris brilliantly saved Gundogan's effort from the spot, but Sterling got to the rebound before him and went tumbling to the floor.
Furious Spurs players were accusing him of diving and VAR decided there had been no foul.
Zinchenko and Toby Alderweireld were booked for their parts in the aftermath, but Sterling was not adjudged to have dived and escaped again.
City should have gone ahead early in the second half, but missed two gilt-edged chances in quick succession.
First, with Lloris out of position, Aguero had a shot cleared off the line by Alderweireld and then from the follow-up Gundogan blazed over from six yards with the goal at his mercy.
The game was changed on the hour as City were finally reduced to 10 men, with Zinchenko picking up a yellow card after cynically stopping the breaking Harry Winks.
Spurs needed only three minutes to take advantage as they took the lead with their first shot of the match.
It was a dream moment from Bergwijn as he controlled Lucas Moura's pass with his chest and sent a low volley into the bottom corner.
The hosts doubled their lead with their next shot eight minutes later.
Tanguy Ndombele slipped in Son and he shot into the bottom corner from the edge of the area, with the help of a slight deflection.
City pushed for a way back into the game, but Kevin De Bruyne's curled cross was superbly tipped over by Lloris, while Sanchez headed against his own crossbar at the death.