Derek Riordan had a goal disallowed for offside in the 38th minute, helped Liam Miller's second-half volley onto the bar and then had a point-blank effort saved by David Crawford late on as Hibs failed to breach the visitors' defence.
Ayr, who showed an enthusiasm and work rate lacking in their hosts, claimed a deserved draw to heap further misery on Hibs boss Colin Calderwood and could have won it only for substitute Andy Rodgers to be denied by Mark Brown in stoppage time.
Stranraer-born Calderwood played for Ayr in his youth and must now take Hibs to Somerset Park for a replay.
Hibs have now won two - both wins coming in November - drawn three and lost seven of their 12 games under the former Scotland defender and if their slump continues it is feasible they could be playing Ayr again next season, should United win promotion to the First Division.
It does not get any easier either for Hibs - with Clydesdale Bank Premier League leaders Celtic visiting Easter Road next week.
Calderwood made two changes to the team which began last weekend's 1-0 loss to Hearts in the Edinburgh derby, with Danny Galbraith and Merouane Zemmama starting.
Zemmama was making his first start since March 27, when he suffered a cruciate knee ligament injury against Falkirk, but played the second half of last month's 2-2 draw with Dundee United.
Calderwood watched Ayr defeat Dumbarton last Sunday in their first match since November and was wary of the threat posed.
United had players with cup pedigree too, in centre back Eddie Malone, who scored the winner for Clyde when they dumped out Celtic on Roy Keane's debut in January 2006, and midfielder Ryan McCann, who played in the 2008 Scottish Cup final for Queen of the South.
McCann shot wide following a poor Paul Hanlon clearance either side of Hibs pressure.
The hosts failed to trouble Crawford in the visitors' goal - behind which United fans had set off a flare which appeared to spark a small fire which was quickly extinguished - and Scott McLaughlin dragged an effort wide at the other end.
Riordan had the ball in the net following Steven Thichot's through ball but the effort was ruled out for offside.
Riordan then thrashed an effort off target and Darryl Duffy shot wide soon after.
Crawford was quickly off his line to deny Riordan after Zemmama's ball over the top as Hibs had to settle for a goalless first half.
Kevin McBride replaced Ian Murray at half-time, with Riordan inheriting the captain's armband.
Crawford blocked a Miller effort after Duffy scrapped for the ball in the visitors' box and Zemmama shot wide on the resumption.
McBride was booked for sliding in on William Easton after 61 minutes before McCann sliced wide after a poor back-pass from Francis Dickoh had sent him through one-on-one with Brown.
Jonathan Grounds' foul on Roberts soon after earned Ayr a free-kick on the edge of the area and McLaughlin curled just over from the resulting set-piece.
Duffy turned and had a shot blocked by Martyn Campbell, the ball appearing to touch the defender's hand while he was on the ground but the referee's view obstructed. There were no appeals from Hibs.
It was Duffy's last action as Valdas Trakys came on and Zemmama was replaced by David Wotherspoon with 15 minutes remaining.
Miller's volley from the edge of the area was helped on by Riordan, skimming the top of the bar, before Wotherspoon shot over from the edge of the area.
Riordan saw a free-kick turned around for a corner by Crawford, who saved another Riordan effort from close range after Galbraith's strong run.
Ayr could have won it on the break in the third minute of stoppage time, but Brown saved after Rodgers had made space for a shot, but Hibs survived and exited to more boos after another poor result.