The result means the north London side are now only four points behind the fourth-placed Blues in the Premier League table.
That gap was as big as 11 points when Mourinho replaced the sacked Mauricio Pochettino in November.
After an inconsistent run of form under the Portuguese the team are showing signs that they can mount a serious challenge once again.
That is despite still being without Harry Kane, who has been ruled out until April with a hamstring injury.
Debutant Steven Bergwijn, signed for £25.4m last week from PSV Eindhoven, scored the first against City, while the return of Hugo Lloris has been a big plus.
Tottenham travel to Stamford Bridge on February 22 to take on rivals Chelsea for what should be a blockbuster Premier League clash.
“We have over 10 games now,” said Son. “We have a lot of games to play but at the end of the season we will see what happens. We just try to be focused. We just try to get as many points as possible.”
Tottenham, who host Southampton in their FA Cup fourth round replay tomorrow night, next play in the Premier League a week on Sunday when they go to Aston Villa.
On the City win, Son added: “Manchester City are so good and played so well in the first half. We had to defend all together but in the second half we came out strong.
"To win today, before the winter break, was very good for our confidence. The fans were so happy and the players as well after the game so it was an important one to win."
On Bergwijn's opening goal and the celebrations: "Steven scored an amazing goal and did a good job. It was emotional because it was his first goal.
“I’m so happy for Steve to score on his debut. It was well deserved and with the emotion he showed it looked great."