With the help of a goal scored in the 13th minute by Gabriel Amato, Rangers had a comfort zone from which to operate and Charlie Miller made sure with the second goal five minutes from time. A corner fell nicely to the substitute, whose shot whistled past a cluster of bodies into the net.
On the kind of rain-soaked night that often favours the smaller club, Rangers took an early lead to help them settle into the tie. Amato collected his free-kick, turned away from his marker and fired a low shot past Craig Nelson, recalled by Ayr after David Castilla had taken the blame for Saturday's defeat by Hamilton.
Rangers were without Andrei Kanchelskis and looked instead to the pace of Rod Wallace and Amato to steal behind the home defence, but despite their First Division status Ayr displayed enough composure to channel the ball through their midfield to Andy Walker, the former Celtic player.
Glynn Hurst, signed from Emley, saw his long-range shot pushed over the bar in the 29th minute and the winger should have done better than fire the ball over the bar from close range from the resultant corner.
Barry Ferguson, through whom Rangers channelled most of their moves, had two long-range efforts, one of which was well saved while the other flashed wide of the post.
Rangers, who had replaced Jorg Albertz with Miller at half- time, were forced into another switch four minutes later when Craig Moore limped off after a tackle with Walker. Colin Hendry came on and immediately saw Walker find space to shoot, although his weak effort did not trouble Lionel Charbonnier.
In the 55th minute, Wallace came close to adding to Rangers lead when he found space at the edge of the area, but his powerful shot was deflected to safety.
Ayr United (4-4-2): Nelson; Robertson, Craig, Walsh, Miller; Hurst, Davies, Millen, Findlay; Lyons, Walker (Ferguson, 75). Substitutes not used: Traynor, Kelly.
Rangers (4-4-2): Charbonnier; Porrini, Moore (Hendry, 50), Amoruso, Vidmar; Johansson, B Ferguson, Van Bronckhorst, Albertz (Miller, h-t); Wallace, Amato (I Ferguson, 86).
Referee: McCurry (Glasgow).Reuse content