Liverpool were held to a frustrating 1-1 draw against West Bromwich Albion on Sunday at Anfield.
Jurgen Klopp's side also suffered another injury concern when Joel Matip limped off with a groin injury in the second half.
West Brom earned their first point under new boss Sam Allardyce but remain in the relegation zone.
By half-time, Liverpool had enjoyed 87% possession and no West Brom player had completed more than eight passes.
The Reds looked to be going five points clear at the top of the table when Sadio Mane chested down Joel Matip's long ball forward to fire past Sam Johnstone.
Liverpool dominated for long periods without adding to their lead but the Baggies improved after the break and equalised in the 83rd minute.
Ajayi leapt high above the home defence to send a header in off the post to spark jubilant celebrations from the away team at Anfield.
West Brom keeper Johnstone made a superb save to deny Roberto Firmino a winner near the end.
"When you go slack you get what you deserve," Andy Robertson told Sky Sports. "When you come up against a Sam Allardyce team you know they will stay in it and take the one chance they get.
"We created chances in the first half and then in the second half it was as if we didn't want to do it again. Every one of us made a mistake in the second half which can't happen.
"We will take the point and move on. We can't dwell on it but it's a huge disappointment."