The Potters moved into the top half of the Premier League table following the victory at Villa Park on Sunday.
Christian Benteke gave the home side the lead early on with his 11th goal of the season, but Peter Odemwingie brought Stoke back level as he chested Crouch's header down and sent it through Brad Guzan's legs with a close-range finish.
Less than five minutes later, Crouch handed Stoke the lead as he poked the ball home from the centre of the 18-yard box before Steven Nzonzi added their third just before the break and Geoff Cameron netted their fourth late on.
Man of the match Crouch told Sky Sports 1HD: "It was very pleasing the way we played, considering we were a goal down.
"At the start of the season we might have collapsed but we showed we've definitely improved.
"We passed the ball really well and we controlled pretty much the majority of the game and came out deserved winners."
Odemwingie, who joined the club in the January transfer window, said he is enjoying his time at Stoke and praised his strike partner Crouch.
"I'm really enjoying it," he said. "It's a great group, I'm really happy off the pitch as well and they have received me very nicely.
"I was really happy playing in the same team as Peter, I knew I would get balls off him and the quality he possesses and it makes things easier for us around him.
"I knew he was going to win the ball in the air so I lifted it a bit - believing he was going to win it - and he did and I kicked the ball and scored.
"That's what I was planning before coming to Stoke."
After going down to Benteke's opener, Odemwingie admitted he felt confident the Potters would come back after being in a similar situation against Southampton last month.
He added: "We've done this before, at Southampton (we were) 1-0 down to an early goal with the game against West Ham, the same thing.
"We're really pleased not to drop our heads and we kept going. We got an early equaliser which helped as well.
"Our overall performance I think was fantastic."Meanwhile, Villa boss Paul Lambert was disappointed his "second best" side lost their lead, and would not make excuses for them.
Villa lost Karim El Ahmadi and Andreas Weimann to injury within a minute of each other in the first half, but Lambert said on Sky Sports 1: "We were definitely second best. That wasn't good enough.
"We got off to a really good start, within five minutes things were looking okay - we lost a couple of lads to injury, Andy and Karim - but (beside that) we were still second best.
"We had a really good start and got a really good goal, but the goals we lost were really, really poor.
"We take nothing away from Stoke, they deserved to win the game.
"(The injuries) do disrupt you a little bit but I'm not going to use that as an excuse."
Next up for Villa is a trip to Manchester United next weekend and Lambert is confident his side can put in a good display following last week's 1-0 victory over league leaders Chelsea.
He added: "We'll be really up for it. Like the Chelsea game, no one expects us to get anything.
"It's a great game to play. As a footballer you want to play these sort of games and it's up to us to try to get something from them."