It is not an illusion, though I would not call it momentum. When a team manages to over-come their rival out of nowhere they gain confidence and start to get better during the match. It has much to do with the moral of the team and how self-awarenesd they have on being able to win the match.
Also, considering this phenomenon exists, we could also talk about how loss of momentum is also a thing: when a team starts playing well but slowly starts to committ mistakes and after mistakes and they lose confidence on their coming victory.
It is something which can be exploited by wise gamblers to make profit, but it takes very good analysis in order to realize when a team is about to win or lose that "momentum".