Vermaelen's own goal gifted the visitors, who had not won at Arsenal in 25 attempts, the lead on 65 minutes.
The Belgian redeemed himself when nodding in from close range with seven minutes left, but the Gunners could not conjure up a winner.
The hosts had dedicated the game to the Save the Children charity, but there was no sense of generosity as Arsene Wenger's men went in search of a sixth straight league win to continue their resurgence.
Andrey Arshavin - one of two changes from the midweek Champions League win over Borussia Dortmund - latched onto a pass from Robin van Persie to slot home, only to see the early celebrations cut short by an offside flag.
Fulham goalkeeper Mark Schwarzer then palmed away a close-range effort from Aaron Ramsey after another sweeping Arsenal attack.
Fulham did pose some threat on the counter, but Arsenal were soon back on the offensive as Theo Walcott scampered away down the left before seeing his shot blocked by a wall of white shirts on the edge of the Fulham box.
On 20 minutes, Bobby Zamora turned Vermaelen just outside the area and drove an angled shot over the crossbar.
Walcott then skipped away again, leaving John Arne Riise trailing in his wake before pulling the ball back to the penalty spot where Ramsey crashed it high into the Clock End.
England winger Walcott was Arsenal's main outlet, this time shooting from the angle with Schwarzer saving at his near post.
Another determined run from Walcott forced a corner before his chip to the far post was nodded back by van Persie and Arshavin was stretching as he hooked the loose ball wide.
Despite all their possession, Arsenal were unable to break down a solid rearguard from the visitors, and Gunners goalkeeper Wojciech Szczesny had to beat away a fierce drive from Mousa Dembele.
Ramsey was close to connecting with Walcott's cross from the right as again Arsenal threatened with half-time looming.
Fulham midfielder Dickson Etuhu was then shown a yellow card for clattering Mikel Arteta and Per Mertesacker's backward header from the free-kick flew just wide.
At the start of the second half Walcott continued to stretch the Fulham defence, as his low cross caused momentary confusion between former Gunner Philippe Senderos and Schwarzer before the loose ball was eventually hacked clear.
Arsenal captain van Persie had been in brilliant goalscoring form, but after battling to create space in the box and slot past Schwarzer he saw his effort hacked off the line by Chris Baird.
Fulham continued to defend resolutely and snatched the lead on 65 minutes through an unfortunate own goal from Vermaelen.
Arteta thought he had been fouled, but play continued and Danny Murphy chipped the ball into the box.
Riise collected the pass on his chest, but the ball then bounced on the penalty spot before being scuffed back past Szczesny into the far corner by the retreating Vermaelen.
Zamora then quickly fired home again, only to be flagged marginally offside.
Arsenal had to step things up and were denied an equaliser when Schwarzer - once a target for the Gunners - clawed away a goalbound header from Johan Djourou after a corner.
The home side continued to press and were finally level when Vermaelen redeemed himself with a close-range downwards header on 83 minutes after Walcott's cross from the right.
Both Gervinho and then Walcott should have produced better finishes when weaving into the box instead of shooting tamely at the keeper.
Van Persie hit the sidenetting when through down the right, and despite all of their late pressure, the Gunners had to make do with just a point.