Old boy Arnautovic denies Twente win
Theo Janssen put the hosts in front with 15 minutes to go when he struck from close range after good work by team mate Marc Janko.
Former Twente striker Marko Arnautovic equalised five minutes later, setting up a combination with Claudio Pizarro before blasting the ball into the net.
"I am satisfied that we came from behind but based on our second-half performance we could have got more out of the game," said Werder coach Thomas Schaaf.
The visitors had to bring on substitute goalkeeper Sebastian Mielitz in the 37th minute after Tim Wiese sustained a knee injury.
Werder are third in the group with two points from three games, the same haul as bottom club Twente. Inter Milan lead the way with seven points followed by Tottenham Hotspur on four.
"Against their strong midfield I thought it was necessary to reinforce my midfield otherwise we would have got run over," said Twente coach Michel Preud'homme.