Leverkusen, enjoying their best start to a season with 15 matches without a loss, lacked their usual offensive spark against the hosts' tight defence and missed their best chance when Stefan Kiessling's header was cleared on the line.
The result lifted Leverkusen to 31 points after 15 matches with second-placed Werder Bremen, on 27 points, able to close in to within a point if they beat lowly Cologne on Sunday.
"We were missing some things today," Leverkusen coach Jupp Heynckes told reporters. "We lacked precision and some good passing and we did not have confidence in midfield.
"It was a strange game with several goal chances. In the end this result is fair although Hanover were maybe a bit better than us."
Bayern Munich edged past Borussia Moenchengladbach 2-1 on Friday to move into third place also on 27 points. Fifth-placed Schalke 04 take on bottom-placed Hertha Berlin on Sunday.
Leverkusen dominated possession early in the first half but were quickly made to work hard as Hanover grew in confidence.
The visitors had a chance to take the lead through midfielder Toni Kroos who seemingly had wrong-footed Florian Fromlowitz, but the Hanover keeper just managed to get a foot to it.
ON THE LINE
The keeper was beaten midway through the second half when Bundesliga top scorer Kiessling headed towards goal before defender Konstantin Rausch cleared the ball on the line.
Hanover could have snatched victory with 10 minutes to go but Hanno Balitsch failed to beat keeper Rene Adler from close range.
Borussia Dortmund extended their unbeaten run to eight league games when they crushed Nuremberg 4-0 with two early goals through Kevin Grosskreutz and Argentine Lucas Barrios.
Mohamed Zidan fired in after a Barrios shot was punched away and Mats Hummels added another on the hour to complete the rout that lifted Dortmund to seventh place on 24 points.
Hamburg SV, in fourth place on 25 points, failed to close in on the top spots, sharing the points with Hoffenheim in a lacklustre goalless draw.
