The Gunners were 1-0 down at Old Trafford thanks to Bruno Fernandes' free-kick when Rice slammed home a leveller in the second half to make it 1-1.
An emphatic strike, Rice was keen to celebrate in front of the Stretford End by shushing the home fans and pulling out Cristiano Ronaldo's iconic 'calma' celebration.
Speaking after the final whistle, the England midfielder explained the reason for goading the United fans and said: "I think it's just a bit of football banter between me and the fans."
But while he and his teammates were enjoying the moment, one teammate was having none of it.
Rice was seen hugging Myles Lewis-Skelly and Mikel Merino, but further away was a furious Gabriel Martinelli.
READ MORE ON FOOTBALL
Man United must build around ageing Bruno Fernandes but still need to sign five players
Arsenal's new sporting director signed Rodri for £16.5m and sealed bargain Suarez deal
The Brazilian forward was screaming at Rice to stop celebrating and get back in position to restart the game.
Clearly not content with a draw, Martinelli wanted his teammates to get the game back underway as soon as possible so that they could chase a winner to keep their Premier League title aspirations alive.
Speaking on commentary, Gary Neville said: "I think Martinelli is right. Get back to the halfway line. He's shouting at Rice 'why are you celebrating?'"
Unfortunately despite the forward's best efforts, Mikel Arteta's side had to settle for a point as any hopes of catching Liverpool drifted even further.
Most read in Football
Iconic 12,000-seater EFL stadium with 'a pub on every corner' now unrecognisable
Club Brugge player causes furious on-pitch mass brawl with controversial gesture
Man United must build around ageing Bruno Fernandes but still need to sign five players
Mikel Arteta walks out of interview as he refuses to answer question in awkward moment
While still having a game in hand, Arsenal are now 15 points behind Arne Slot's side with Liverpool looking like runaway favourites to claim the crown.
It means that for the Gunners it could be another season where they fail to go all the way and cement themselves as the top team in English football.
talkSPORT BET: Latest Cheltenham Festival odds and free bet offers
After the game at Old Trafford, Arteta tried to leave his interview with Sky Sports reporter Patrick Davison early in a clear show of his frustrations.
The Spaniard had been non-committal when asked if his team's lack of striking options had hindered their title aspirations.
Arteta then tried to leave, before Davison pushed once again.
"Mikel, one more," he said as the Spaniard tried to dart away.
"I have to ask you about the title race because it's 15 points now, is it too much?"
Arteta replied: "Alright, thank you," before departing the scene.
Arsenal are next in action on Wednesday night when they look to finish off the job in their Champions League round of 16 clash with PSV - a tie that they lead 7-1.
They then return to Premier League action next Sunday as they host fellow top four challengers Chelsea.