Artur Sobiech's neat finish and an own goal from Twente skipper Peter Wisgerhof completed an unlikely comeback for Mirko Slomka's side who, at one point, were 2-0 down after goals from Willem Janssen and Nacer Chadli.
Up against it
Perhaps showing the after-effects following their blistering start to the Bundesliga campaign, Hannover fell behind with just seven minutes on the clock as Twente's Janssen fired under Ron-Robert Zieler from close range. Left-back Konstantin Rausch was struggling to keep tabs on the roaming Roberto Rosales, whose inviting right-wing cross was glanced wide by the lively Dusan Tadic, who prodded over moments later.
The Eredivisie leaders continued to make life difficult for the Reds, with centre-backs Trevizan Felipe and Mario Eggiman fortunate to see Luc Castaignos dink over after exploiting a gaping hole left by the defensive duo. An injury to Sergio da Silva Pinto hardly helped matters for Slomka's charges, who had to wait the best part of half an hour to register their first effort on goal as Szabolcs Huszti sent a 20-yard free kick straight at goalkeeper Nikolay Mihaylov.
Hannover raised the tempo following the restart, but Chadli's deflected free kick after a foul by Steven Cherundolo on the edge of the box left Zieler rooted to the spot and the Reds seemingly with a mountain to climb.
Against all odds, a similar spot of fortune saw Sobiech pounce on Rausch's deflected strike to reduce the arrears in the 67th minute, with Twente, for the first time, looking second best. Pushing forward at will, Hannover duly levelled six minutes later as Wisgerhof could only direct Rausch's inviting cross past his own keeper. Castaignon could have won it for Twente, but Zieler twice stood his ground to ensure a point apiece.
Twente Enschede: Mihaylov - Rosales, Douglas, Wisgerhof, Braafheid (50. Boyata) - Janssen, Brama, Schilder (46. Landzaat) - Tadic, Castaignos, Chadli (77. Gutierrez)
Hannover 96: Zieler - Cherundolo, Felipe, Eggimann, Rausch - da Silva Pinto (31. Nikci), Andreasen (75. Schmiedebach) - Stindl, Huszti - Schlaudraff, Abdellaoue (46. Sobiech)
Goals: 1:0 Janssen (7.), 2:0 Chadli (54.), 2:1 Sobiech (67.), 2:2 Wisgerhof (73., own goal)