Slavisa Jokanovic’s men created a number of good chances but were unable to find the net and were punished when Anderson struck the only goal of the game in the 76th minute.
Jokanovic made one change to his starting line-up, with Morgan Gibbs-White returning after suspension in place of Oli McBurnie.
Blackpool head coach Neil Critchley named an unchanged starting line-up.
An early effort from Oliver Norwood saw the United midfielder’s long-range shot clear the bar.
Iliman Ndiaye found the net with an 11th-minute header, but the home side’s celebrations were cut short by an offside flag.
Blackpool threatened when James Husband got to the left-hand byline and played the ball across the face of goal, with Jerry Yates just failing to get a touch.
Josh Bowler then played a free-kick into the area which evaded everyone, and goalkeeper Robin Olsen did well to dive at full stretch and turn the ball wide of his right-hand post.
The home side then had a couple of good chances, with Lys Mousset firing straight at Daniel Grimshaw before Ndiaye shot wide from inside the area after a great through ball from Gibbs-White picked out his run.
Gibbs-White had a low shot saved by Grimshaw in the opening minute of the second half, and the Blackpool keeper then produced a superb save to keep out another effort from the same player.
As the hosts continued to apply pressure, Mousset saw his shot strike the underside of the bar before being cleared.
A double substitution for the visitors saw Bowler and Yates replaced by Demetri Mitchell and Sonny Carey.
A change for the home side followed, with David McGoldrick taking over from Ben Osborn.
George Baldock fired over from just inside the area as the home side looked to capitalise on their dominance, before Blackpool threatened on the break, with Anderson’s deflected shot turned wide by Olsen.
McGoldrick then had a goal-bound shot blocked, but the hosts then lost Mousset to injury.
After Carey’s drive was deflected over, Blackpool scored in the 76th minute when Anderson received the ball and cut inside and curled the ball into the roof of the net.
Jokanovic sent on striker McBurnie in place of midfielder John Fleck to bolster the attack, but United never threatened to equalise.