Steven Davis wrapped up the victory with a goal of his own in the 83rd minute to help Ireland move up a spot in Group C, which puts the nation five points behind leaders Germany.
Azerbaijan have been the surprise package of the qualifying group, having headed into the game on the back of a three-match unbeaten run and as many clean sheets.
As the game progressed, the Green Army took control and dominated the ball, with McAuley coming close to finding the breakthrough when he met the ball at the back post from a free kick, but his header across goal was cleared.
At the other end, Ramil Sheydaev's close-range shot was blocked, but Azerbaijan's goalscoring opportunities became few and far between in the first 45 minutes.
McLaughlin and Josh Magennis were getting plenty of joy down the right-hand side, and the former managed to find space before crossing into the box for Shane Ferguson, whose volley smashed into the side-netting.
Ireland caused problems for their opponents with long throws into the box, one of which bounced for Chris Brunt, but the West Bromwich Albion player ended up nodding the ball directly to the goalkeeper.
There was some concern as Brunt, who was making his first international appearance for 13 months, suffered a head injury while leaping for a header, but after being bandaged up on the sidelines, he was given the green light to continue.
After knocking on the door, the hosts found their way in through Lafferty, who caught the ball on the half-volley and sent it into the back of the net from 12 yards out.
O'Neill's side continued their dominance and doubled their lead five minutes before half time from a deep free kick, which was delivered into the box by Brunt.
McAuley rose the highest in the box to meet it and directed a powerful header past the keeper to give the Green Army a two-goal cushion at the break.
Azerbaijan posed more of a threat at the start of the second half as they searched for an equaliser, with Ismayilov's through-ball reaching substitute Deniz Yilmaz, but the goalkeeper rushed out to block the shot.
Shane Ferguson tried to capitalise on a poor back pass by latching on to the loose ball and crossing for Oliver Norwood, whose 25-yard shot was blocked.
Ireland had to soak up some pressure from the visitors, who came close to finding an equaliser when the ball dropped to Arif Dashdemirov's feet on the edge of the box, but as he leaned back to take a strike, the ball ended up soaring above the crossbar.
Azerbaijan's dominant spell did not last long, though, as Ireland tripled their lead from a set piece. Norwood's delivery found McLaughlin at the near post and the defender headed home off the woodwork.
In the 83rd minute, Steven Davis helped in Brunt's low strike with a flick, which capped off a successful night for the Green Army.