Having drawn the fixture the Gunners remain in the hunt but an injury to Fabregas on the stroke of half-time does little to improve their prospects.
Rafael Benitez, whose team have already beaten Chelsea and Manchester United this season, missed the game as he recovers from surgery to remove kidney stones but the Liverpool boss did pick the team.
Keane, an unused substitute against Hull last weekend, returned as one of four changes from the team that drew with the Tigers.
Steven Gerrard played just behind the Irishman and the two combined after 10 minutes for the opening opportunity of the game. Keane looked to be yards offside as he collected a long ball but Gael Clichy had played him on and the striker laid the ball off to Gerrard, whose shot from 20 yards was saved by Manuel Almunia.
We would have won with 11 men - Wenger
Arsenal took time to settle, struggling to play their fluent passing game. However, Adebayor forced a save from Pepe Reina with a header after he met Bacary Sagna's cross from the right.
And Van Persie put Arsenal ahead with a goal of individual brilliance.
Nasri, returning after injury, picked out the Dutch forward with a raking pass but Van Persie was closely marked by Jamie Carragher and Daniel Agger as he brought the ball down on his chest.
Van Persie created a yard of space with his second touch and smashed the ball into the corner of the net with his third.
Clear-cut chances remained at a premium but it was another moment of brilliance that saw Keane equalise with his third Premier League goal of the season.
Van Persie's goal was the product of brilliant skill and control
Arsenal had been troubled previously by long balls upfield and failed to deal with an optimistic punt over the top from Agger that Keane smashed home spectacularly on the half-volley.
Liverpool might have led at the break but Gerrard could not quite find the target after sliding in to meet a low cross from Kuyt, who then went close himself with a low shot across goal that Almunia did well to save.
And the half ended on a sour note for Arsenal when skipper Fabregas sustained a knee injury challenging Xabi Alonso for the ball and was replaced by Vassiriki Diaby.
Keane enjoys Liverpool strike
Leiva Lucas tested stand-in captain Almunia with a strike shortly after the resumption and the home team's travails worsened when Adebayor was dismissed.
The striker had his foot raised as he competed with Alvaro Arbeloa and caught the defender with his elbow as he spun, prompting referee Howard Webb to issue a second yellow card.
But Arsenal, who had struggled since the resumption, rallied after losing Adebayor and enjoyed a spell of pressure in and around the Liverpool box.
However, it was Liverpool who came close to a late winner, with a long-range strike from Agger narrowly missing the target and Nabil El Zhar heading wide.
Arsenal: Almunia, Sagna, Djourou, Gallas, Clichy, Denilson, Fabregas (Diaby 46), Song Billong, Nasri (Eboue 90), Adebayor, Van Persie.
Subs Not Used: Fabianski, Vela, Ramsey, Silvestre, Wilshere.
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