The Irishman headed home the clincher on 60 minutes after Nicky Law had opened the scoring at Somerset Park 30 seconds into the second half.
The victory over the Honest Men - Rangers' 23rd league win of the campaign - maintains their 23-point lead over nearest challengers Dunfermline.
And the numbers keep stacking up for Ally McCoist's side, who can now clinch the title with just five more wins, provided the Pars do not slip up before their potentially decisive Ibrox clash on March 15.
Rangers were sloppy in the first period and had Cammy Bell to thank that they were not behind at the break.
But a faster tempo and improved passing display following the interval saw the Glasgow giants through in the end.
McCoist had to reshuffle his back four as a result of the suspensions being served by centre-halves Lee McCulloch and Bilel Mohsni.
Brazilian Emilson Cribari came in for just his third start of the season as Sebastian Faure moved to the middle of the back four while Richard Forster returned at right-back.
And there was a shaky moment for the new-look defence inside the first two minutes as Alan Forrest - younger brother of Celtic winger James - wriggled into space on the by-line to tee up former Ibrox hitman Kevin Kyle.
Bell was there with a smart stop, though, and the keeper did even better 10 minutes later as he sprang to his left to push away a dipping Craig Malcolm volley fizzing towards the top corner.
Rangers threatened seriously for the first time after quarter of an hour as David Templeton sent stand-in skipper Lee Wallace sprinting down the left. The full-back found Dean Shiels with his cut-back but the Northern Irishman's shot at David Hutton was tame.
Ayr were testing the Ibrox side's makeshift back-line with a series of dangerous corners but while Rangers just about clung on, there was enough menace in the deliveries to have McCoist worried.
But again the Gers manager had his number one to thank on the half hour as Bell saved brilliantly down to his left after Michael Donald was somehow allowed to gather Brian Gilmour's corner before smashing a shot from 10 yards out without a player in blue in sight.
It was a let off but the visitors should have responded with an instant sucker-punch. They broke swiftly up field as Shiels powered forward before rolling in Fraser Aird.
The Scottish youth international's strike cannoned off the bar but there was a red face waiting for Law after the midfielder skied the rebound with the net gaping.
Malcolm then wasted another Ayr chance by blasting wide from 18 yards as Rangers continued to look sloppy at the back.
But whatever McCoist said to his team at half-time, it worked as within 30 seconds of the restart they grabbed the lead. Ayr failed to clear their lines and that let in Aird to buzz a dangerous ball across the face of goal for Law to bundle home.
Malcolm came close again with a low shot but Rangers went up another gear as Daly beat Hutton to Wallace's tempting cross to nod home the second.
The fight went out of the home side after that and only a decent stop from Hutton prevented substitute Andy Little adding a third for the Light Blues in the closing stages.