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".
It doesn't take much analysis to identify a team that is gaining grounds in a sports. In football you will observe that the ball possession had changed and the shots on and off target are now increasing. The statistics of the game is always available during the games.
However, we shouldn't be deceived by a momentary recovery of a club because it could change within few minutes. The technical team of the other club might identify the lapses and correct then immediately which could now lead to better performance. To avoid all these uncertainties and distractions, I just place my bets ad forget about them. It's doesn't matter the team that is impressing, I am just focused on the winner