But it was City that started the strongest, with Micah Richards, playing at right-back, linking up dangerously with Shaun Wright-Phillips.
Fabio Collocini had to snuff out danger from that pair on 10 minutes, just before Newcastle midfielder Geremi went close with a 25-yard free-kick awarded after Tal Ben Haim hacked down Obafemi Martins.
Controversy exploded soon after, as Ireland nodded down for Wright-Phillips to instantly knock a beautifully weighted through-ball into the path of Robinho beyond Newcastle's back-line.
Beye turned and, in challenging to clear from the Brazilian, touched the ball before making contact with Robinho.
Kinnear hopes the red card will be rescinded
But referee Styles pointed to the spot and sent Beye off, leaving Newcastle's players and crowd seething with rage before Robinho wrong-footed Shay Given to convert the penalty with aplomb.
With numerical advantage, City controlled possession, while the home crowd aimed their anger at Robinho and Styles, who earlier this season had apologised to Bolton for making a mistake in awarding a penalty against them.
Interim manager Joe Kinnear moved Martins out to the left wing, leaving Ameobi alone upfront where he battled hard to win free-kicks from which Geremi occasionally threatened.
City created openings but did not test Given, and were made to pay two minutes before half time.
Martins swung a cross in but, as Dunne cleared, the ball deflected off Vincent Kompany and Ben Haim into the path off Ameobi who chested the ball forward and finished awkwardly for his first goal in over two years.
Penalty decision helped Magpies - Hughes
No changes were made at the break, and with Newcastle competing well, City were restricted to a couple of long-range efforts.
And with manager Mark Hughes fuming on the sidelines, Newcastle took an unlikely but perhaps deserved lead in the 63rd minute.
Geremi swung over a dipping corner and, as the ball arched rapidly towards his feet, Dunne failed to adjust his body and volleyed the ball into the top corner of his own goal.
That forced Hughes to bring on Ched Evans for Dietmar Hamman, and the young Welsh striker immediately forced Steven Taylor into a superb block to deflect a shot over the bar.
Kinnear made a defensive substitution in the 75th minute, bringing Charles N'Zogbia on for Martins, and though City continued to threaten, it seemed Newcastle might hold on for an unlikely win.
But City's one-man advantage told in the end as Ireland latched onto Robinho's through-ball to slip it past the on-rushing Given, leaving Newcastle second from bottom.
Newcastle interim manager Joe Kinnear:
"It was a fantastic performance from 10 men. I couldn't ask for more.
"We were totally committed, played some decent football and created more of the clear-cut chances.
"I thought we'd just about hold on but there were a lot of tired legs. The good thing was we didn't get beaten and we've come out of it with a lot of credit and a point."
Manchester City boss Mark Hughes:
"We played some good stuff in the opening period, creating chances with the angles of our runs and we were in good shape.
"I expected us to go on and win the game comfortably. But the sending off seemed to help them. We found it easier to open them up when it was even player-wise.
"We had to dig in and get back into the game. But we'll look back on this game and performance as three points lost."
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