It took less than two minutes for Martin O'Neill's side to take the lead as Long ended a 17-match goal drought for club and country, latching on to Wes Hoolahan's through-ball before keeping his composure to pick out the bottom corner.
The visitors were very much on the front foot during the opening stages, but failed to add to their lead despite further chances for McClean and Long.
The openings soon began to dry up, though, and Moldova's rearguard action looked to have worked when they equalised right on the stroke of half time. Ireland were caught high up the pitch as Bugaev raced through on goal before finishing with aplomb to open his side's qualifying account.
The hosts started the second half brightly too, but Ireland soon regained the upper hand and McClean and Hoolahan both had sights of goal in quick succession inside the opening 10 minutes of the half.
It wasn't until the 69th minute that they regained the lead, though, and this time McClean made no mistake when picking out the bottom corner after Jonathan Walters had somewhat fortuitously guided the ball into his path.
Any worries that Moldova - who have now lost seven matches in a row - may respond again were appeased seven minutes later when McClean doubled his personal tally for the night, this time steering Seamus Coleman's low cross home to give his side a valuable cushion.
That proved to be enough for Ireland to take all three points from the first ever meeting between the two sides, moving above fellow home nation Wales in the Group D standings.
O'Neill's side are now joint top along with Serbia on seven points, while Moldova remain on zero and have now won just one of their last 23 matches.