Liverpool, who were knocked off the top of the table by United on Saturday after seven weeks in the lead, appeared all set to reclaim the spot after a superb Steven Gerrard goal put them ahead after 68 minutes.
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Gerrard lashed in a low 30-metre drive that skidded across the surface and eluded Tim Howard as Everton conceded their first goal in six league matches.
Everton struck back in the dying minutes when Mikel Arteta swept in a perfectly flighted free-kick and the unmarked Cahill got ahead of the Liverpool defence to glance in the equaliser.
The draw, Liverpool's fifth in 11 league matches at Anfield, saw them pull level with Manchester United on 47 points but the champions stay top on goal difference and now have a game in hand. Everton remain sixth with 36 points.
"When you are top of the table and you are winning with three minutes to go (and draw) -- you have lost two points," Liverpool boss Rafa Benitez told Setanta Sports.
"I thought we had all the control in the second half and more possession, but to concede a goal three minutes from time like that you have to be disappointed."
Everton scorer Cahill told Setanta: "We needed that point and for us and our fans it's a massive result."
MEET AGAIN
Liverpool were made to pay for not taking their chances earlier and Fernando Torres, making his first start for the club since November following an injury, had an excellent chance to put them ahead in the 28th minute after a stunning 60-metre pass from Sami Hyypia split the Everton defence.
Torres timed his shot to perfection, but with only Howard to beat from six metres out, fired against the goalkeeper's left-hand post and the ball bounced wide.
Everton's best chance of the opening half had come two minutes earlier when Cahill climbed to meet Victor Anichebe's cross and saw Pepe Reina tip the ball to safety.
Liverpool had the first real scoring chance after the break when Gerrard forced Howard into another important save and Everton defender Leighton Baines thwarted Hyypia as the ball rebounded to the marauding Finnish defender.
Everton's players thought they had a claim for a penalty just before Liverpool scored when Anichebe appeared to be brought down by Martin Skrtel but the referee waved play on.
Torres also claimed a penalty when he seemed to be sent tumbling by Everton defender Phil Jagielka but Jagielka said afterwards: "I think he shimmied, gone to one side, gone back into me and gone over. Thankfully the ref saw it that way."
The two sides meet again at Anfield in an FA Cup fourth-round tie on Sunday.
