Bunney continued his fine run of goalscoring form in the 12th minute after turning home a Jim McNulty cross.
Dale had to defend for the majority of the second half but weren’t troubled until stoppage time, when substitute Wesley Burns came inches away from an equaliser as he hit the underside of the bar.
Keith Hill made one change to the starting line-up from Saturday’s 2-2 draw at Bradford City. Reuben Noble-Lazarus replaced Nathaniel Mendez-Laing, who dropped to the bench.
The opening ten minutes were quiet and not really in keeping with a feisty first half, which was kicked into life with Bunney’s fourth goal in three games.
Michael Rose picked out McNulty’s overlap, and the Dale defender delivered a low cross to the near post which Bunney turned past Chris Maxwell.
Matty Lund’s curling effort flew well wide as Dale looked for a quick second, whilst at the other end Josh Lillis was out quickly to deny former Newcastle United striker Shola Ameobi an equaliser.
Bunney had half a chance to double his tally for the night when he was found in the area by Jamie Allen, but he didn’t connect properly with his volley on the turn before it was cleared behind for a corner kick.
Proceedings threatened to boil over when Ian Henderson was booked for a late challenge, with Fleetwood goalkeeper Maxwell also cautioned for racing from his goal to remonstrate.
Challenges were flying in half-time approached, with the visitors coming close to equalising on a few occasions. Ameobi had an effort superbly blocked by Niall Canavan making his home debut, before the striker fired just past the far post when he broke into the area.
Ashley Hunter also came within inches of finding the back of the net with a snap effort after Antoni Sarcevic had his shot blocked inside the area.
The majority of the second half was relatively uneventful compared to the first. The visitors dominated possession as they attempted to play out from the back, but the Dale defence were hardly troubled. McNulty made a great block from former Dale man Bobby Grant’s shot, whilst substitute Burns fired well over just after coming on.
Grant Holt made his second home debut for Dale when he came on for Bunney just after the hour mark, whilst David Syers replaced Noble-Lazarus in a double switch.
Syers came close not long after coming on with a half volley from the edge of the area, but his effort was always rising.
Peter Vincenti replaced Lund with ten minutes remaining to try and help see out the one goal lead.
Holt almost made the points safe six minutes from time, but Maxwell beat away his effort at the near post after a neat back heel from Syers.
There were a minimum of four minutes added for Dale to battle through, but Fleetwood came agonisingly close to an equaliser in the first of those. Burns headed against the underside of the bar from a corner, before his effort on the rebound was deflected over from inside the six yard box. The resulting corner fell to Burns again, but he sent his effort over the bar again.
That would be the last chance for either side, as Dale held on for a hard earned three points.