Erwin van de Looi's side would have climbed above Ajax and AZ, both in action on Sunday, into third with a win but instead they required two late goals to rescue a point and extend their unbeaten run to seven league games.
Danny Verbeek put the home side ahead in the 10th minute and when substitute Stipe Perica doubled the lead with 15 minutes to go it looked a lost cause for the visitors, but Giliano Wijnaldum pulled one back with 10 minutes remaining before De Leeuw's spot-kick ensured the spoils were shared.
A place and two points behind Groningen are Heerenveen, who came from behind to win 3-1 at home against Go Ahead Eagles.
Erik Falkenburg put the away side in front two minutes before the break, only for Marten de Roon to equalise three minutes into the second period.
Pele van Anholt completed the turnaround four minutes later and Hakim Ziyech rounded off the scoring six minutes from time to condemn the visitors to their third defeat in four.
PEC Zwolle drew their fourth successive game, 1-1 at home to RKC Waalwijk, Mustafa Saymak breaking the deadlock on the stroke of half-time for the hosts before Aurelien Joachim earned his side a share of the points with a goal six minutes into the second half.
Elsewhere, Utrecht came from behind to beat Heracles 2-1.
The hosts went in front courtesy of Iliass Bel Hassani's 27th-minute goal, but Jens Toornstra struck in the 55th and 81st minutes as Heracles fell to a third successive defeat.
