Cole nicked a goal late on for the 1-0 win.
Ivanovic, for whom goalscoring has never been a problem, said: "For me, Ash is the best left-back in the world - for a long time.
"He is really great, and always makes a lot of good things for the team.
"We're really happy for him because, for defenders, it is always nice to score goals for the confidence. Ashley is really fantastic.
"He has the skill, he has the speed, he can run, he can go up front, he has the vision of the game, he defends well, he is quick. But I think all this is nothing new!
"When he is ready, and his ankle is all right, he is the best.
"He can go on running a lot - I think more than other players."