Benevento were awarded a penalty with barely five minutes gone, as Gianluca Lapadula was bundled over by Ivan Radovanovic, and Nicolas Viola coolly sent Mattia Perin the wrong way to open the scoring.
Yet just minutes later Genoa were level, as Goran Pandev took advantage of a sloppy clearance in the box to blast in from close range at the near post.
An incredible opening quarter of an hour saw Benevento regain their advantage through a stunning Lapadula goal against his former club, with the Peruvian dancing through the box before rifling into the top corner.
Pandev drew the hosts level once more midway through the first half however, as he pounced on a deflection to find space and fire into the far corner.
Genoa were brighter in the second half and striker Mattia Destro came close with powerful effort from range, whilst Adolfo Gaich saw a deft header go inches wide at the other end.
In a half of few clear chances, Eldor Shomurodov and Pandev threatened but the Grifone couldn’t find a way through.
The point leaves Benevento hovering above the relegation zone in 17th, whilst Genoa move up to 14th in the table.