Brentford 1 Southampton 3
Brentford got off to the perfect start when Ed Hutchinson scored after just five minutes to put the League One side ahead. But Saints striker Crouch equalised just six minutes later.
The Bees dominated the game for long periods but were dealt a cruel blow midway through the second half when Phillips scored - and Crouch added a last-minute goal to kill off any hopes of a comeback.
A sell-out Griffin Park crowd were given early hope of a shock when Martin Allen's side made a bright start.
With just four minutes on the clock, Hutchinson had a good chance but failed to hit the target.
But 60 seconds later he made amends as he tapped home a rebound after Paul Smith had saved from Jay Tabb.
Saints needed to hit back quickly, and they did just that as Crouch levelled in the 11th minute. Phillips' close-range volley was parried only as far as Crouch who pounced to knock the ball home.
Before the break, Brentford had chances to regain the lead and Hutchinson came closest when his 34th minute header hit the bar.
After half-time, the pace of the game picked up and Tabb had a good chance which he put wide.
But it was the visitors who eventually took the lead in the 67th minute. A quick breakaway left Brentford chasing shadows and Southampton midfielder Matt Oakley found Crouch in a space on the right. The lanky striker's quick cross found Phillips at the far post for an easy tap-in.
Brentford tried to find an equaliser but Southampton ended their hopes of playing Manchester United in the next round when substitute Neil McCann crossed for Crouch to net his second of the game.