The Australia international was unfortunate to deflect home a Luuk de Jong header that rebounded off the post, against the goalkeeper, and in.
While Fulham's unbeaten European record at Craven Cottage remains intact, manager Martin Jol will have been frustrated to draw with the club he once played for.
The west Londoners impressed throughout and took the lead courtesy of Andrew Johnson, who finished with aplomb after latching onto Dwight Tiendalli's square ball.
Despite a performance that belied their poor Premier League showings, Schwarzer's own goal forced the teams to share the points at the end of the Group K encounter.
Much of the talk heading into the game was about Bryan Ruiz, who joined the Cottagers from Twente on transfer deadline day but was ineligible to face his former club.
The absence of the Costa Rica international was one of six changes following the weekend's 1-1 draw with Blackburn, with debutant Zdenek Grygera the most notable inclusion.
Twente, who started the season in the Champions League qualifying stages, made one alteration to the side that lost 2-1 at Roda JC on Saturday, replacing top scorer Marc Janko with Roberto Rosales.
After a tentative start, the visitors had the first shot on goal after eight minutes through Ola John, brother of former Fulham striker Collins John, but Schwarzer saved the tame effort easily.
Fulham looked the brighter of the two teams during the opening exchanges and, after seeing a couple of chances thwarted, Clint Dempsey went close.
The United States international jinked through the middle and unleashed a low drive that former Liverpool reserve goalkeeper Nikolay Mihaylov did well to parry, before the defence cleared.
Dempsey and Mousa Dembele were having a lively start to the game and the latter blazed over shortly after as the Cottagers upped the ante.
The pressure paid off after 19 minutes when Johnson intercepted a pass across the back by Tiendalli and flicked past Mihaylov.
Fulham continued to press the Twente backline after taking the lead, with Danny Murphy going close after collecting Brede Hangeland's superb looping ball from the halfway line.
Despite the home side's dominance, the 2009/10 Dutch champions still showed flashes of class and De Jong was unlucky to see a powerful header saved by Schwarzer.
Fulham were made to pay for their inept finishing in the 40th minute when Twente levelled.
Minutes after Schwarzer superbly saved a long-range Willem Janssen effort, De Jong's header bounced off the post and rebounded into the net off the back of the goalkeeper's head.
The second period started relatively slowly before bursting into life when Dempsey headed Pajtim Kasami's cross just wide at the back post.
The effort spurred the home side on and, after a few good moves broke down, Johnson forced Mihaylov into a quick reaction save after a melee in the box.
Fulham fans felt Dempsey should have been awarded a penalty in the build-up and were further frustrated when the Texan then saw an effort saved after a fine run from Dembele.
The Whites were looking far more creative than they have done so far this season and continued to attack, with Steve Sidwell flashing a header over as the match entered the final 20 minutes.
With their former manager Steve McClaren watching on, Twente came into the game more as they searched for a first win against English opposition in 12 attempts.
However, wayward finishing and resolute defending from Fulham kept the Enschede-based side at bay as the match petered out, earning the sides a point apiece.