Ian McCall, the Ayr manager, praised his players’ approach after they negotiated a potentially tricky afternoon to claim their place in the Championship play-off final.
United already held a three-goal advantage from the first leg in midweek and adopted attack as the best method of defence as they went on to increase their margin of victory.
McCall said: “I’m happy at how we handled the occasion. We knew we had one foot in the final but I wanted us to attack and not sit back and we couldn’t afford any complacency as we lost two late goals at home to Airdrie last week.
“We were also aware of Rory McAllister’s threat as he hit five goals in one game against Falkirk but Jamie Adams handled him superbly.”
Ayr had an early scare when goalkeeper Greg Fleming was forced to make a brave save, diving at Steven Noble’s feet.
Rory McAllister also had a half chance for the Blue Toon but shot over from 12 yards after Ryan Strachan headed on Noble’s corner.
At the other end Ayr went close when Michael Donald’s cross was met by a firm header from Ross Docherty and Graeme Smith dived to save.
The hosts increased their aggregate lead on 27 minutes when Robbie Crawford shot low into the right-hand corner of Smith’s net from 14 yards.
Peterhead had a glimmer of hope four minutes later when Leighton McIntosh’s cross deflected off Donald and beyond Fleming.
But it was Ayr who put the issue beyond doubt on 57 minutes when Nicky Devlin headed in Docherty’s corner.
Peterhead manager Jim McInally said: “I’m trying to keep a balanced view of the situation because we didn’t lose the game today – it was because of what happened the other night. It has been a bizarre season with so many good things, including a 19-match unbeaten run and a cup final against Rangers.”