City, top of the table for the first time since the premier league was formed 10 years ago, have seven points from three games, one ahead of Arsenal, Manchester United and Chelsea who have all played a match less. Blackburn slipped a place to fifth.
"It could have gone either way but it was a terrific game of football and we edged it in the end," Keegan told Sky Sports. "All in all we got what we deserved."
German midfielder Michael Tarnat earned the visitors an early lead with a stunning free kick from 35 metres out in the fourth minute.
But the first half ended in confusion when a mix-up between former England and Arsenal goalkeeper David Seaman and Trevor Sinclair, both new signings, led to the midfielder heading into his own net from a corner to level the score.
Blackburn piled on the pressure after the break, but it was City who retook the lead in the 59th minute when midfielder Joey Barton dribbled through the Rovers defence before slotting past Brad Friedel from inside the penalty area.
Two minutes later, however, defender Lorenzo Amoruso scored his second premier league goal for his new club when another error from Seaman allowed the Italian to score with a glancing header from Brett Emerton's corner.
French striker Anelka grabbed the winner three minutes from time, breaking clear of the defence before producing a deft shot from a tight angle that slipped through Friedel's legs.
