Denilson then fired over and Phil Neville magnificently blocked Thomas Vermaelen's shot as Everton stood firm.
He reacted quickly after home keeper Boaz Myhill had palmed out Denilson's swerving shot.
Roque Santa Cruz was wayward with the hosts' best chances before Adebayor headed in Denilson's cross unmarked.
At that point it was all going wrong for Arsenal, who will wait to see the extent of Denilson's problem.
Romario and Ronaldo are exhilarating to watch and Denilson could also prove to be one of the best players in the tournament.
Denilson put the Gunners ahead on four minutes after Nicklas Bendtner's pass.
The second-half had a frantic start as Eboue claimed a penalty and Denilson picked up a booking for a nasty two-footed tackle.
First-half goals from Samir Nasri and Denilson set the Gunners on their way to the knockout stage for a 10th campaign in succession.
Arsenal ended the half in charge, with Boruc turning Eduardo's left-foot shot to safety and Bendtner heading the resulting corner from Denilson inches wide.
BBC: SPORT | Football | Europe | Arsenal 3-1 Celtic (agg 5-1)
However, Wenger said that he expects Denilson and Abou Diaby to be fit for Arsenal's final pre-season match, against Legia Warsaw on 7 August.
Arsenal initially struggled to make their numerical advantage tell and Denilson's yellow card for a mistimed tackled on Tevez summed up their early rustiness.
After a spell of Arsenal pressure, Eduardo laid the ball back to Denilson and his effort from outside the box hit Osman and wrongfooted Howard.
Nasri struck from six yards after four minutes following Denilson's cutback.
Owen Coyle's side then doubled their advantage from the penalty spot through Matthew Taylor after Arsenal midfielder Denilson had fouled Lee Chung-yong inside the area.
Arsenal are also currently without the injured Gael Clichy and Denilson.
The chance came after Denilson collapsed in a heap, with no-one around him, gifting Everton possession, and it is unclear what caused the Brazilian to fall.
In the 73rd minute, Denilson burst away from the halfway line to score the third and Edilson made it 4-0 from close range five minutes later.
However, Gunners goalkeeper Manuel Almunia saved Alessandro Diamanti's resultant penalty to preserve the lead given to the home side by midfielder Denilson in the fifth minute.
Arsenal also lost Russia forward Andrei Arshavin and France defender William Gallas to calf injuries, while Brazil midfielder Denilson and defender Gael Clichy are also doubtful.
Arsenal clawed their way back into the game with a slice of good fortune as Denilson's shot took a deflection off Osman to leave Tim Howard stranded.
Johan Djourou and Denilson are available to face Bolton on Saturday after injury, while Sebastien Squillaci could be involved for the first time after his move from Sevilla.
Then, in first-half stoppage time, Denilson crashed home the second goal from 30 yard out, the ball swerving through the air to give goalkeeper Sinan Bolat no chance.
In contrast, Arsenal's flagging form was epitomised when the disappointing Denilson played team-mate Laurent Koscielny into trouble with a weak pass across the face of his team's penalty area.
Holding midfielder Denilson was particularly wasteful in possession but others were culpable too, and it was not until the 25th minute that the visitors created a chance of any note.
Arsenal dominated possession thereafter but rarely looked like breaching the home defence and it was hardly surprising to see Denilson replaced by Marouane Chamakh as Wenger switched from 4-5-1 to 4-4-2.
The Baggies had still to find any sort of rhythm when they were cut apart by a smooth interchange of passes involving Bendtner, Gael Clichy and Denilson that led to Nasri's opener.
Walcott, Bendtner, Tomas Rosicky, Denilson and Laurent Koscielny have all recently returned from injury and they helped the visitors make a blistering start against a Newcastle line-up chosen with Sunday's Tyne-Wear derby against Sunderland in mind.
It was a passing display so typical of Arsene Wenger's side, and it was no surprise when Adebayor made it two on the stroke of half time, the Togo international heading home unmarked from Denilson's cross.
But when Chamakh was brought on for Denilson - Wenger replacing a holding midfielder with a striker - the substitute almost had an immediate impact, only for Mignolet to deny Arshavin after the Moroccan's run and pass from right.
Brazilian midfielder Denilson fired Arsenal's opener from the edge of the penalty box before headers from new defender Thomas Vermaelen and William Gallas stunned the home side, who had been hoping to break into the top-four this season after finishing fifth in 2008-09.
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