Blackpool boss Ian Holloway made 10 changes from the side that drew 2-2 with Everton at the weekend but they were arguably the better team before Stewart Downing put the hosts ahead with a deflected shot in the 28th minute.
Villa old boy Marlon Harewood levelled just before half-time and, after Nathan Delfouneso had netted his first of the season on the hour mark, DJ Campbell stunned Villa Park with Blackpool's second three minutes from time.
But Villa went straight down the other end to secure the three points through Collins' header.
It was Blackpool who began the brighter, with 19-year-old winger Matt Phillips twice playing in Harewood but both times the striker was denied by alert Villa defenders.
The hosts also had their chances in an open start to the game and Luke Young might have done better than fire over the angle of post and bar following a nice move involving former Blackpool loanee Barry Bannan and Delfouneso.
Blackpool ramped up the pressure again and it needed a good challenge from Luke Young to deny Harewood, but in the 28th minute it was Villa who took the lead through Downing.
The winger played a lengthy one-two with Ashley Young before turning on the edge of the area and sending in a shot that flew past Richard Kingson with the help of a deflection off Dekel Keinan.
Villa were suddenly finding a lot more space and Blackpool were lucky to survive on a couple of occasions, firstly when Luke Young shot over from 15 yards and then a cross-shot from Marc Albrighton that was hacked clear by Jason Euell from just in front of his own goalline.
But on the stroke of half-time Blackpool grabbed an equaliser. A brilliant back-heel from Phillips played in Harewood and the former Villa man calmly slotted past Brad Friedel and just inside the far post.
Harewood had more reason than most to celebrate his goal after struggling to make an impression during three years with Villa prior to joining Blackpool this summer.
It was the hosts who were first on the attack in the second half and Kingson was fortunate not to concede a second when he misjudged Ashley Young's 20-yard shot but did just enough to push it wide of the post.
From the corner, Collins saw his header cleared off the line by Rob Edwards while at the other end Harewood rose well to meet a corner but headed wide.
The impressive Phillips then went on a run through the heart of midfield and his stinging shot would have caused Friedel major problems had it not been straight at the American.
Blackpool were finding Downing's corners tricky to deal with and from another inswinger Richard Dunne powered his header onto the top of the bar.
In the 55th minute Villa thought they had retaken the lead when Ashley Young streaked away down the right and crossed for Delfouneso to head into the far corner. It looked a good goal but referee Anthony Taylor penalised the striker for a push on Keinan.
Villa had their tails up, however, and Delfouneso only had to wait five minutes to get on the scoresheet, the 19-year-old seizing on a precision pass from Ashley Young and tucking away his shot.
Blackpool could have no complaints and they appeared lucky not to give away a penalty moments later when Albrighton tumbled under a clumsy challenge from Edwards.
Delfouneso's work for the evening was done and a great cheer from the Villa Park crowd greeted the arrival of Gabriel Agbonlahor, after five weeks out injured, with 26 minutes left.
Holloway sent on leading scorer Charlie Adam in place of Euell and he almost made an immediate impression with a 25-yard free-kick, given after Stephen Warnock had hacked down the charging Phillips, that was deflected just wide.
Villa should have made the game safe with 10 minutes to go as Downing tore down the left flank before picking out the unmarked Albrighton at the far post, but he shot into the ground and over the bar.
It looked like they would be made to regret that miss with three minutes left when, out of nothing, substitute Campbell equalised with a shot from the edge of the box that caught Collins and looped up and over Friedel.
But less than two minutes later the Blackpool's fans were silenced as Collins squeezed his header just inside the post from Downing's corner, and this time there was to be no comeback from the visitors.