Rice bagged his first goal for the club since his £105million move from West Ham with a fierce effort which crept inside the post after United had failed to clear a corner. Sub Jesus wrapped up a big win with a cool finish on the counter-attack.
United took the lead against the run of play in the first half when Marcus Rashford finished brilliantly off the inside of the post but Arsenal hit back straight from kick-off through Martin Odegaard's crisp strike.
The VAR was at the heart of a controversial second half, with referee Anthony Taylor reversing his decision after awarding Arsenal a penalty for an Aaron Wan-Bissaka foul on Kai Havertz. United sub Alejandro Garnacho then thought he had won it in the 88th minute, only to be ruled fractionally offside.
Here's how we rated the Arsenal players...
Made an important save from Anthony Martial at 1-1. Could only get a fingertip to Rashford's opener, though it was a terrific strike.
Dealt well Onana's diagonals and got forward to join the attacks. But Rashford stepped inside him to open the scoring.
Gabriel Magalhaes 7
Passing was mixed but solid enough defensively. Managed to play Garnacho offside by a fraction late on.
Made a crucial goal-saving block to deny Rashford at the start of the second half and eased Rasmus Hojlund off the ball in a dangerous area late on. Lucky Garnacho's goal was ruled out after being dragged out of position.
So good at playing the free role, popping up all over the pitch and was involved in the build up to Arsenal's equaliser.
Declan Rice 8
Capped an imposing display with a late, late strike to kickstart his Arsenal career.
Martin Odegaard 8
Finished first-time superbly to level the game. Looked a threat with the ball at his feet.
Kai Havertz 5
Fluffed an early chance with a disastrous air-shot and lost possession in the build-up to United's goal. A frustrating outing was exacerbated when referee Anthony Taylor overturned the decision to award him a penalty.
Always a threat with the ball and saw a couple of fierce efforts well blocked. Lucky to avoid a red card for a studs-up challenge on Bruno Fernandes.
Always a threat against Wan-Bissaka in a great battle down the left flank. Squared for Odegaard's equaliser.
Worked hard and linked the play, including in the build-up to Odegaard's goal. But offered little in the way of goal-threat.
Gabriel Jesus (Nketiah 76') 7
Took his goal superbly with a cool turn and finish.
Takehiro Tomiyasu (Zinchenko 76') 6
Kept it simple in an tnverted full-back role.
Fabio Vieira (Havertz 76') 7
Used the ball well in a late cameo, including with the pass for Jesus' strike.
Reiss Nelson (Martinelli 90') 7
Full of direct running in eight minutes of stoppage-time and won the ball in the build up to Arsenal's third.
Jorginho (Odegaard 90') N/A