Rovers laboured for large parts of the first half before Bradley Dack’s opener in first-half stoppage-time for his third goal in as many games.
Armstrong, League One’s player of the month, netted for the fourth successive home game with two after the break – a stunning curling effort and a clinical finish to take his Rovers tally to seven.
The league leaders are unbeaten in their last seven matches and Mowbray was delighted with Armstrong’s contribution.
He said: ‘He’s a young guy who’s come from a Premier League club and with total respect to League One, his attributes of speed, ability to shoot off both feet, awareness of space, he’s better than League One.
‘But here he is playing for us and we’re delighted. It’s fantastic he could help finish the game off like he did.
‘He’s a young lad learning the game. I’m sure Rafa Benitez will see all his video clips of every game, see the fact he’s scored a lot of goals over the last few weeks.
‘Two brilliant strikes today – the first one planted into the top corner and the second one a cutback on the move. He works extraordinarily hard.
‘It’s not as though he’s a striker who stands up there and waits for chances. I’m delighted he’s here, delighted he’s helping the team be successful and I look forward to him scoring many more goals.’
Blackpool boss Gary Bowyer cut a frustrated figure after the Tangerines saw their five-match unbeaten run end.
He felt his side were denied a penalty in the first half and questioned the award of the free-kick which led to the opener.
He said: ‘I never buy into this ‘it’s never a 3-0 performance’ or anything like that. The result will always say what it is.
‘However, that said, I don’t know what we have to do to get a penalty this year. I’ve just watched it back and the lad’s arm was waist high when he handballed it.
‘The referee tells me it’s down by his side and I’ve just seen it back. It’s a clear handball, and at 0-0 when we started the game ever so well, it’s just so frustrating because they have a big impact on the game.
‘Is it a foul between (Danny) Graham and (Curtis) Tilt for the free-kick when he puts it in? Don’t get me wrong, I’ve said to our lads we have to defend the free-kick better, but they are two big, major decisions that have had a massive impact on the game and he’s (the referee) not done anything.’