The visitors took an unexpected lead after just four minutes when Robbie Crawford beat three men on his way to an excellent solo goal.
Hibs went on to dominate possession, but they were out of sorts and struggled to create clear chances.
Even once they equalised, Hibs were unable to secure a win, wth Grant Holt's header cleared off the line.
The result nudges Hibs nine points clear of Dundee United, who can reduce the gap at home to Raith Rovers in the evening kick-off.
Hibs suffered their setback early enough to initially consider it an inconvenience. The home fans were stunned when Crawford gathered the ball 25 yards out, to the right of the penalty area, then set-off on a run towards goal.
He might not have had a plan in place, but his impetuosity took him into the danger area, and past three challenges as he jinked and weaved with the ball. Eventually, he was in a position to shoot and his low effort seemed to bobble underneath the outstretched hand of goalkeeper Ross Laidlaw.
The home side have to have been resilient enough to respond, but there was a lacklustre quality to their play. Even with two fast wingers in Chris Humphrey and Martin Boyle, they failed to turn the Ayr defence.
Passing was laboured, and there were symbolic moments across the field, such as James Keatings tackling his own team-mate, John McGinn, on the edge of the Ayr penalty area and Lewis Stevenson throwing the ball straight to an opponent deep inside his own half.
There were inevitably half-chances, given how much possession Hibs enjoyed, but Andrew Shinnie's effort at the near post from Keatings' cross was blocked by Ayr goalkeeper Greg Fleming. Just before the interval, Shinnie also headed over.
Hard words would have been spoken in the home dressing room, and Humphrey didn't reappear as Hibs boss Neil Lennon sent on Holt.
Soon after the restart, Hibs' top scorer, Cummings, also made his way off the bench. By then, the home side were utterly dominating the ball, but Ayr were defending manfully and Nicky Devlin headed off the line.
The pressure eventually told, though, as Cummings applied the finishing touch with his head to Keatings' cross.
There was a desperate search for a winning goal, with Cummings' long-range effort pushed away and Holt's header cleared off the line by Brian Gilmour. Ayr, though, held on.
Hibernian manager Neil Lennon: "The first-half performance was awful and the goal we conceded was symptomatic of the way we played. The second half was a lot better, so I'm pleased we showed a bit of character to get something out of the game. It feels like we dropped a couple of points, no question.
"Our build-up play was poor, pedestrian, looked like there was a bit of panic out there at times. I don't know where that's come from. In the second half we made a few changes and got the goal we deserved and on balance should probably have won.
"We forced the game in the second half, but I wanted that from the first whistle. We gave them all the warnings before the game about how difficult it could be, I don't know if they ignored me or just didn't settle into the game the way I wanted them to.
"I'm not interested really in the [Scottish] Cup [tie at Hearts] yet. I'll concentrate on that next week. It was all about today and I'm disappointed that we didn't go on to win."
Match ends, Hibernian 1, Ayr United 1.
Second Half ends, Hibernian 1, Ayr United 1.
Foul by Grant Holt (Hibernian).
(Ayr United) wins a free kick in the attacking half.
Corner,  Hibernian. Conceded by Patrick Boyle.
Foul by Fraser Fyvie (Hibernian).
Conrad Balatoni (Ayr United) wins a free kick in the attacking half.
Attempt missed. John McGinn (Hibernian) left footed shot from outside the box is close, but misses the top left corner.
Corner,  Hibernian. Conceded by Robbie Crawford.
Attempt saved. Grant Holt (Hibernian) right footed shot from the centre of the box is saved in the top right corner.
Corner,  Hibernian. Conceded by Greg Fleming.
Attempt saved. Jason Cummings (Hibernian) left footed shot from outside the box is saved in the top left corner.
Attempt missed. David Gray (Hibernian) header from the centre of the box misses to the right.
Foul by Brian Graham (Hibernian).
Ross Docherty (Ayr United) wins a free kick in the defensive half.
Substitution, Hibernian. Brian Graham replaces Martin Boyle.
James Keatings (Hibernian) is shown the yellow card for a bad foul.
Foul by James Keatings (Hibernian).
Ross Docherty (Ayr United) wins a free kick in the attacking half.
John McGinn (Hibernian) wins a free kick in the defensive half.
Foul by Michael Rose (Ayr United).
Attempt saved. David Gray (Hibernian) header from the right side of the six yard box is saved in the centre of the goal.
Substitution, Ayr United. Michael Rose replaces Gary Harkins.
Goal!  Hibernian 1, Ayr United 1. Jason Cummings (Hibernian) header from the centre of the box to the bottom right corner. Assisted by James Keatings.
Attempt missed. Fraser Fyvie (Hibernian) right footed shot from outside the box misses to the right.
Corner,  Hibernian. Conceded by Patrick Boyle.
Attempt missed. Darren McGregor (Hibernian) left footed shot from the centre of the box is just a bit too high.
Corner,  Hibernian. Conceded by Patrick Boyle.
Attempt saved. Jason Cummings (Hibernian) right footed shot from the left side of the box is saved in the bottom left corner.
Substitution, Ayr United. Craig McGuffie replaces Paul Cairney.
Hand ball by Ross Docherty (Ayr United).
Foul by Darren McGregor (Hibernian).
Declan McDaid (Ayr United) wins a free kick on the left wing.
Attempt saved. David Gray (Hibernian) right footed shot from the right side of the box is saved in the bottom left corner.
Substitution, Hibernian. Jason Cummings replaces Andrew Shinnie.
Attempt missed. Martin Boyle (Hibernian) header from very close range is close, but misses to the left.
Attempt missed. John McGinn (Hibernian) left footed shot from outside the box is close, but misses to the left.
Foul by Grant Holt (Hibernian).
Conrad Balatoni (Ayr United) wins a free kick in the defensive half.
Foul by John McGinn (Hibernian).
Championship leaders Hibernian needed a Jason Cummings header to rescue a point against second bottom Ayr United.