The diminutive striker, on loan from Newcastle, struck in the 15th and 61st minutes and would have rounded off his day with a hat-trick but for a shot hitting a post.
Armstrong had seen little of the ball in the opening exchanges but in the 15th minute he sprang to life.
Jim O’Brien spotted Armstrong’s run and played the perfect through-ball into his path and the striker finished coolly.
It was the perfect start, but only served only to fire Wigan up as Coventry goalkeeper Lee Burge was forced to make a good save from Will Grigg in the 17th minute.
But too often the lone Wigan striker was left isolated and the visitors were unable to capitalise on a fair share of possession.
Grigg had another chance just before the half-hour mark when Burge came for a cross he had no hope of making, but the striker could not bring his header down low enough.
Wigan reshuffled after the break but it came to nothing as Armstrong subtly guided home his second goal from John Fleck’s cross.