Gibson lashed home his first goal since quitting Old Trafford earlier this month as the Barclays Premier League leaders slipped up at Goodison Park.
The visitors hit the bar in the first half through Samir Nasri but Everton, who earlier saw a Denis Stracqualursi effort cleared off the line, again proved stubborn opposition for City.
City had won just one of their previous 13 league visits to Everton and the extension of that poor record left them top of the table only on goal difference.
Manager Roberto Mancini was again frustrated by another controversial decision as his team were denied a late penalty for handball by Phil Neville but referee Peter Walton ruled any contact accidental.
It was an eventful contest which also saw a bizarre interruption when a protester chained himself to a goalpost.