Jesus, 19, marked his full home debut for City by scoring twice, including a 92nd-minute winner, to give Pep Guardiola's side a 2-1 win over Swansea City that lifted them up to third.
Mkhitaryan scored one goal and made another in a 3-0 victory at relegation-threatened champions Leicester City that took United to within two points of the top four.
Jose Mourinho's side remain sixth, a position they have occupied since November, but Arsenal, beaten 3-1 by leaders Chelsea on Saturday, and Liverpool, stunned 2-0 by Hull City, are now within reach.
City are 10 points behind Chelsea and a point below second-place Tottenham Hotspur, with Arsenal two points back, one point above fifth-place Liverpool and two above United.
After three successive league draws, Mourinho changed tack for the trip to the King Power Stadium, bringing in Juan Mata for Michael Carrick and ditching his usual 4-1-4-1 system for a 4-4-2.
But United, who were missing Wayne Rooney through illness, looked off their game until a switch to a 4-2-3-1 formation mid-way through the first half.
The move brought Mkhitaryan into the number 10 role and he put United ahead in the 42nd minute, beating Robert Huth to Chris Smalling's header on halfway and sprinting clear to score.
Less than 90 seconds later it was 2-0 as Zlatan Ibrahimovic expertly steered Antonio Valencia's cross past Kasper Schmeichel for his 20th goal of the season.
Mkhitaryan turned creator as United put the game to bed five minutes into the second half, facilitating a one-two with Mata that freed the Spaniard to beat Schmeichel at his near post.
It was Leicester's 13th defeat of the campaign and kept Claudio Ranieri's men a slender point above the relegation zone.
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Manchester City's Gabriel Jesus scores one of his two goals against Swansea City at Etihad Stadium REUTERS
Jesus needed just 11 minutes to crown his full home debut for Manchester City with a goal as he put Guardiola's men in front against Paul Clement's improving Swansea.
Martin Olsson prevented Raheem Sterling from applying the finishing touch to David Silva's low cross, but Jesus pounced to volley the loose ball past Lukasz Fabianski.
City completely dominated the first half, but took their foot off the pedal after the break and were punished when Gylfi Sigurdsson swept in a low, left-foot equaliser in the 81st minute.
But Jesus had the final say, tucking the ball into the net at the second attempt after his header from Silva's right-wing cross had been parried by Fabianski.
Swansea remain a point above the relegation zone, below Leicester and Middlesbrough on goal difference, and Clement felt his side had been unfortunate not to come away with a point.
Leicester City 0 Manchester United 3
(Mkhitaryan 42, Ibrahimovic 44, Mata 49)
Manchester City 2
(Jesus 11, 90+2) Swansea City 1
P W D L GD Pts
24 19 2 3 34 59
24 14 8 2 30 50
24 15 4 5 20 49
24 14 5 5 24 47
24 13 7 4 22 46
24 12 9 3 15 45