The Togo striker picked up a second yellow card when he was accused of elbowing Alvaro Arbeloa after earlier picking up a soft booking.
Robbie Keane cancelled out Robin van Persie's 24th-minute goal just before half-time and the Gunners also suffered the loss of captain Cesc Fabregas through injury.
The game began brightly with Liverpool setting themselves up with Keane as a lone frontman. The midfield and defence was packed and the tactic was to soak up any pressure from the Gunners and then pour forward on the break.
Arsenal for their part began the game looking more confident and determined than they have of late. They closed Liverpool down quickly and used possession well.
The first real effort fell to the visitors in the tenth minute when a long ball forward to Keane was knocked back into the path of Steven Gerrard whose first-time shot from the edge of the area was claimed by Manuel Almunia.
His counterpart, Pepe Reina, was called into action for the first time in the 15th minute to claim Adebayor's goal-bound header after the striker had stooped to meet Bacary Sagna's low cross and redirect the ball towards the left-hand corner of the net.
The Gunners took the lead with a sensational van Persie goal. The Dutchman ran on to a diagonal ball from Samir Nasri that was placed between Liverpool's two centre-backs.
Van Persie controlled the ball on the turn and then, in one fluid movement, burst forward to shoot right-footed beyond Reina's dive.
Liverpool were back on level terms in the 42nd minute when Keane latched on to a long ball forward, outpaced Arsenal's slumbering central defenders before shooting first time beyond Almunia and into the roof of the net.
Gerrard should have scored the visitors' second just over a minute later when he slid in to meet Dirk Kuyt's cross into the area, but he redirected the ball high and wide.
Kuyt himself tried his luck in first-half stoppage time and his shot across goal was parried for a corner by the Gunners keeper.
Arsenal suffered a further setback just before the end of the first half when Fabregas was injured after sliding in to make a tackle.
He failed to come out after the re-start and was replaced by Abou Diaby who slotted in to the wide left position.
Denilson moved into central midfield and the Gunners instantly looked devoid of ideas having lost their play-maker and leader.
Arsenal's afternoon got worse after Adebayor was sent off for a second bookable offence by Howard Webb. The first booking on 38 minutes was questionable and the second drew the wrath of the home support.
Adebayor was adjudged to have swung an arm at Carragher who, clutching his face, fell to the ground theatrically. Van Persie was left to lead the line alone, as the home side tried to re-group.
As the atmosphere grew increasingly hostile, the game lost its fluency. Van Persie was stopped from breaking away by a cynical Carragher challenge in the 72nd minute, but the Dutchman went close a minute later with a snap-shot that brought the best out of Reina.
Nasri, who had been quiet for most of the game, suddenly started appearing all over the pitch. His mazy run in the 80th minute required a shot of equal quality, but the Frenchman sliced his effort wide.
Daniel Agger went close in the 86th minute with a 25-yard drive that soared just wide of the top left corner of the Arsenal net but the game finished 1-1 with referee Howard Webb being jeered off the pitch.