Before kickoff, players and fans at Ibrox observed a minute's silence in memory of former Rangers defender Sandy Jardine, who died following a battle with cancer earlier this week.
Peralta tried to set up Daly later in the half, but the striker's finish struck the crossbar.
Rangers took the lead less than 10 minutes before half time when Aird made a solo run from midfield, beating several defenders before beating Mitchell with a powerful finish.
Ally McCoist's side continued to create the majority of the chances in the second half and doubled their lead with less than an hour gone when Peralta drilled it in from the edge of the box.
Aird almost scored a second a few minutes later when he unleashed a curling effort from long range, but it crept just wide.
Dean Shiels put the win beyond doubt in the 64th minute when Steven Smith sent in a through-ball, which he initially headed straight at Mitchell before sliding in to score from the rebound.
The result leaves the already-crowned champions unbeaten at home this season.