Crouch tapped home from 12 yards after a blistering burst of pace from Aaron Lennon unlocked the Milan defence to seal the win with a vital away goal.
The match was nothing like the pulsating 4-3 loss to Inter here in November or the 3-1 Spurs victory in the reverse fixture, but Harry Redknapp will not care one bit.
The home side were lucky to end the match with 10 men after an horrific late lunge from Matthieu Flamini on Vedran Corluka, and some shocking behaviour from Gennaro Gattuso, who appeared to headbutt Spurs assistant Joe Jordan after the final whistle having pushed him in the face during the game following an argument on the touchline.
But Crouch’s goal – his sixth in eight European matches this season – means Spurs take a lead into next month’s second leg.
Four months ago Redknapp saw his side almost complete a remarkable second-half comeback against Inter thanks to Gareth Bale’s hat-trick.
The Welshman was missing on Tuesday night after failing to recover from a back injury.
Niko Kranjcar, who had deputised for Bale so well, was a surprise omission from Tottenham’s starting XI, with Steven Pienaar taking Bale’s usual position down the left flank.
Luka Modric failed to recover from his appendix injury in time and was named among the substitutes.
Two familiar foes were named among the Milan team – former Arsenal midfielder Flamini and Manchester City’s on-loan striker Robinho.
Despite seeing his side collapse against Inter here in October, Redknapp urged his team to stick to their attacking principles and throw everything at the Italians.
Crouch proved to be the visitors’ most potent weapon in the opening exchanges, causing Christian Abbiati to come and punch away a dangerous low cross.
Abbiati picked up a head injury when challenging the tall marksman for the ball and had to be replaced by substitute goalkeeper Marco Amelia.
Milan sounded Spurs a warning with their first real chance 20 minutes in, Robinho bursting down the right and crossing to Zlatan Ibrahimovic but William Gallas jumped in with a decisive clearance.
Milan thought they should have had a penalty 23 minutes in when Sandro clattered into Ibrahimovic but referee Stephane Lannoy waved the protests away.
Michael Dawson went clattering into Ibrahimovic with a raised arm in the box. The Swede went down clutching his head but soon returned to his feet after seeing his penalty appeal turned down.
Flamini was lucky not to be booked for a late sliding challenge on Rafael van der Vaart.
Aaron Lennon turned Luca Antonini inside the box but he sent over a high cross that even Crouch could not get on the end of.
Van der Vaart gained a yard and fired a blistering shot that Amelia tipped over with a brilliant save.
Crouch received a bruising kick to the ribs from Alessandro Nesta’s follow-through towards the end of the half.
The second half began with a period of intense Milan pressure.
Heurelho Gomes Pulled off a superb flying one-handed save to deny Mario Yepes, who rose well to meet Gattuso’s cross.
The game took an ugly turn 55 minutes in when Flamini flew in with a diving two-footed tackle on Corluka which sent the full-black flying into the air.
To the Spurs’ players anger, the midfielder only saw yellow. Corluka had to be stretchered off and replaced by Jonathan Woodgate, who came on for his first appearance since November 2009.
Tempers frayed moments later when Pienaar clattered into Gattuso.
Spurs assistant Jordan was furious with the referee’s decision to give a foul and squared up to the midfielder on the touchline. Both men pushed each other before Redknapp stepped in and they both walked away.
Play eventually resumed after both sets of players remonstrated with each other.
Yepes drew another point-blank save from Gomes with a six-yard header but the centre-half showed his petulant side by needlessly barging into the Brazilian when he went to throw the ball out seconds later.
Van der Vaart, clearly struggling with his calf injury, was replaced by Luka Modric on the hour.
The ugliness continued, Crouch the latest person to clash with Gattuso when he went for a header.
The Milan captain was then finally booked for a late tackle on Pienaar.
Milan pushed for an opener but they were shocked when Crouch broke the deadlock with 10 minutes left.
Lennon raced at the Milan defence with blistering pace, hurdled Yepes’ challenge and squared for the former Liverpool man to tap home from 12 yards.
The hosts pushed for an equaliser but had to resort to long shots as Tottenham held onto the ball well, much to the delight of the travelling 5,000 Spurs fans.
Dawson had to put in a last-gasp tackle to deny Antonini as the game entered injury time before Ibrahimovic thought he had pulled one back with a superb volley but he was adjudged to have pushed Dawson in the box.
The ugly scenes that had marred the match continued after the whistle with Gattuso appearing to head-butt Jordan.