Julien Gorius put Genk ahead in the 20th minute and the home side seemed to be on track to claim their third consecutive win in the tournament before Marcel Sabitzer's late goal saw the points shared.
The result means Genk remained top, ahead of FC Thun, who were beaten 3-0 by Dynamo Kiev in Thursday's other Group G clash.
Vienna's Christopher Dibon had the first real chance of the game when he saw his low shot blocked by Genk defender Kalidou Koulibaly in the sixth minute.
Genk striker Benjamin De Ceulaer then fired a chance over the bar but the Belgian Cup holders did not have to wait much longer to open the scoring thanks to Gorius.
The midfielder found the end of Fabien Camus' short free-kick and took a touch before blasting an unstoppable 25-yard effort into the top corner for his third goal in as many Europa League appearances.
Rapid threatened to equalise eight minutes before the break but Koulibaly blocked Terrence Boyd's header.
Genk remained on course for a sixth straight win in all competitions and almost doubled their advantage in the second half only for the woodwork to deny Katuku Tshimanga.
Sabitzer then claimed a valuable point for his side - the second of the campaign - when he headed in Louis Schaub's cross from close range in the 82nd minute.