The Spaniard returned after missing a couple of games over Christmas to poke home the 93rd-minute winner that sent City 11 points clear at the top of the Premier League.
It was the 25 year-old’s third goal of the season and former City skipper Dunne believes the ex-Atletico Madrid star is irreplaceable.
“He’s like a Rolls-Royce,” said Dunne on Matchday Live.
“He glides around the pitch and what he does looks simple, but he makes whole team tick.
“Rodri has taken that role on, becoming like Sergio Busquets at Barca, spreading the ball around the pitch and getting us going.”
Dunne also believes the manner City secured victory, deep into added time against the Gunners, will have also been a hammer blow to title rivals Chelsea and Liverpool, who meet on Sunday afternoon.
“To go 11 points clear is such a psychological blow for Chelsea and Liverpool, especially when they see result like that and a 93rd minute winner,” said Dunne.
“Even the last few minutes Arsenal were threatening with free-kicks and crosses, but look how Ederson claimed the ball and how desperate Ruben Dias and Aymeric Laporte were to head it away and just clear the lines rather than trying to be too smart.
“We just wanted to win so bad and that has shown through the attitude in second half.
“Obviously, after the red card the momentum changed and we had a lot more possession, but Arsenal were defending brilliantly and were, really solid.
“Our first shot on target in open play was the winning goal when they had 10 men. Credit to Arsenal, defensively they played really well.
“City had more of the ball, but couldn’t find gaps, space and didn’t threaten the goal until the last minute.
“Scoring a goal in the dying seconds is the best feeling in world. It certainly is when you go away to a tough team like Arsenal; they are the best side City have played this season and that’s probably as well as they have played under Mikel Arteta.
“To be able to come through that and win, especially in the last couple of minutes when it feels everything is against you – the whole stadium are against you because the referee has made couple decisions they’ve not liked - it is so sweet to score that goal so late.”
