Arsenal overturned a 1-0 deficit to lead 2-1 at the break, with Gabriel thumping in a header into the back of the net from close range after team-mate Riccardo Calafiori had cancelled out Erling Haaland's opener.
But the Gunners were forced to defend for almost the entirety of the second period after Leandro Trossard was handed his marching orders at the end of the first half following a second booking for kicking the ball away.
Mikel Arteta's team were under the cosh for long periods of the match as City controlled possession and dictated play.
And Timber and Havertz became the first outfield players since Opta records began during the 2003/04 campaign to play 89 minutes or more of a match without successfully making at least one pass to a team-mate. Timber attempted six passes at the Etihad, while Havertz tried to make five, but none of them were successful.
The duo worked their socks off for their side and are likely to be key players for the Gunners this season as the three-time Premier League champions endeavour to win the top-flight title for the first time since 2004.
"We had a very difficult start," Arteta explained in his post-match press conference as he gave his verdict on the showdown. "We struggled to control certain spaces, we didn't have enough ability.
"We adapted to that context in the best possible way. I'm so proud of them. You cannot be given a more difficult situation against that opponent and I'm so proud of my team.
"I prefer not to comment [on the red card]. I was already in big trouble trying to solve what happened on the pitch. It's that obvious that it's not necessary to comment on it. I'm expecting 100 games to be nine vs 10 this season if that's the case.
"I have no clue [if we would have won with 11 players]. We would try for sure. After in the second half we tried. What I can say is 99 times out of 100 if you play against that team with 10 men, you lose."
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