Paul Jewell's side were on top throughout at Portman Road and deserved the three points which leaves Scunthorpe staring at a return to League One.
Caretaker boss Tony Daws took charge of the visitors for the first time after Ian Baraclough was sacked in the aftermath of the 3-0 home defeat to Preston in midweek but saw his charges fail to threaten as they were passed off the Portman Road pitch.
Edwards whistled in a 30-yard drive before the break and the victory was assured by a trademark Bullard free-kick early in the second half.
Scunthorpe are now four points adrift of safety and have just eight games left to preserve their Championship status.
Ipswich captain David Norris was in the side after a surprise recovery from an ankle injury and should have scored in the third minute when he charged into the area but his low shot was kicked clear by goalkeeper Josh Lillis.
Bullard then connected beautifully with a volley on the edge of the box but Iron defender David Mirfin stood strong to make a painful block before Connor Wickham wasted a glorious chance to open the scoring.
Bullard swung in a dangerous free-kick and Wickham was left unmarked at the far post but fluffed his connection and saw his volley spin wide from five yards out.
The visitors were struggling to hang on but had a rare chance of their own when Michael O'Connor saw his free-kick well saved by the recalled Arran Lee-Barrett in the Ipswich net.
Jewell's side were well on top however and there was no surprise when Edwards struck in the 26th minute - although there was plenty of surprise about the manner of the goal.
A miscued defensive clearance from Mirfin was seized on by Edwards charging forwards from right-back and the former Sunderland man thumped a first-time shot from fully 30 yards which flew into the top corner.
It was a stunning strike and captain Gareth McAuley should have doubled the advantage moments later when he fired over from a set-piece.
Lee Martin was the latest to be found guilty of missing a chance as the half ended when he ran onto a sumptuous Bullard pass but dragged his shot wide.
Martin was then booked seconds into the second half for diving as he went down inside the penalty area before Bullard made it 2-0 in the 53rd minute.
Norris was fouled 25 yards from goal and the on-loan Hull man stepped up to bend a fabulous strike over the wall and past Lillis into the corner.
Bullard was running the show and came close to another from even further out moments later but saw his 35-yard drive fly just wide of the left post.
Wickham is in the running for the young player of the year at Sunday's Football League awards and should have celebrated with a goal but the teenager delayed his shot and allowed Eddie Nolan to make a fine tackle.
Town saw out the rest of the game to record a comfortable victory.