Pep Guardiola's men were never allowed to play their normal fluent game and could not respond as a disciplined Chelsea sealed a second Champions League triumph.
Tielemans's goal will count among the finest to win this 149-year old competition.
United's defeat means City are 10 points clear with both sides having three games left to play.
United's win put on hold the title celebrations of champions-elect Manchester City.
With Chelsea looking secure in the top four, the final Champions League place looks to be a three-way fight between Leicester, West Ham United and Liverpool.
Thomas Tuchel continued his stunning impact in west London to become the first coach to reach back to back Champions League finals with different clubs.
City were dominant against PSG, who lost their heads in the second half and finished the semifinal second leg with 10 men after Angel Di Maria was sent off in the 69th minute.
Goals by Kevin De Bruyne and Riyad Mahrez earned them a 2-1 comeback win at Paris St Germain in the semifinal first leg.
For the fourth successive season, Pep Guardiola's side triumphed in the final of the competition on Sunday with a 1-0 victory over Tottenham.
The club’s recent lack of success, Messi's dissatisfaction with the management and many more factors seem to indicate that a departure from the club is on the cards.