Celtic had gone three games without a win in the SPL prior to the clash with the Dons and were initially frustrated as the deadlock remained unbroken until deep into the second half.
Late goals from Lassad Nouioui and Charlie Mulgrew secured all three points, and defender Ambrose admitted it was important stay patient.
The Nigerian said: "To get back to winning is a great feeling. The past two or three games in the league have not been good for us. We've lost points and conceded goals, but this is football.
"We had to be patient and take our chances when they came. The manager asked us to be patient, because the goals would come, even if it took until the 95th minute."
Celtic now head to the Estadio da Luz to face Benfica in Champions League action.
Ambrose accepts his side face a tough challenge but is determined to follow up the historic win over Barcelona with another good result.
"We know the Benfica game is going to be another difficult game for us," he said. "We are going to work hard to maintain the same levels we have been used to in the Champions League.
"We are not going there to lose. They are a good team and they have great fans and a good atmosphere, but they know that Celtic are not just there to be run over.
"We have beaten Barcelona and Spartak Moscow, so it will be a different atmosphere.
"If they lose the game, they are out so we know they're going to give it their all, but we are going to make sure we do the same and not be overawed by the surroundings or the fans."