England striker Crouch struck 10 minutes from time following a swift counter-attack at a rain-soaked San Siro, extending Milan's poor recent home record in European competition to just one win in 10 games.
Serie A leaders Milan, seven-time European champions, struggled to impose themselves in a niggly encounter that flared up at various stages.
Milan midfielder Mathieu Flamini was lucky just to be booked for a crude two-footed lunge that forced Vedran Corluka out of the game and Gennaro Gattuso appeared to headbutt Spurs assistant manager Joe Jordan after the final whistle.
Gattuso had to be pulled away from Jordan and Spurs manager Harry Redknapp branded the Italian firebrand “crazy”. On Wednesday, UEFA said in a statement that its Control and Disciplinary Body would meet on Monday, Feb 21 to discuss the case following “incidents” in the game, which flared up on several occasions.
Spurs had an early shout for a penalty turned down when the fit-again Rafael van der Vaart's effort appeared to strike Alessandro Nesta on the arm.
The home side lost goalkeeper Christian Abbiati after 18 minutes with a head injury.
Raul to the rescue
Raul marked his first match in Spain since leaving Real Madrid with a trademark poacher's strike to rescue a 1-1 draw for Schalke 04 in Valencia on Tuesday.
The 33-year-old striker, who netted Real’s third goal in a 3-0 win over Valencia in the 2000 final, scored just after the hour to cancel out a 17th-minute effort from another former Bernabeu favourite, Roberto Soldado.
His goal extended Raul's record tally in the three major European club competitions to 69 and came on his return to his native country after swapping La Liga for the Bundesliga at the end of last season.
German defender Christoph Metzelder’s mistake put Valencia on top as he surrendered possession in a dangerous position and Jeremy Mathieu crossed for Soldado to clip the ball past keeper Manuel Neuer from six metres.
Raul, then, found space inside the penalty area and drove a low, left-footed shot across keeper Vicente Guaita into the far corner of the net.