The Iceland striker tucked away Christian Poulsen's pass in the 83rd minute just as Groningen seemed headed for a draw.
The win takes Ajax to 47 points ahead of Twente Enschede who won 2-0 at fifth-placed Heerenveen on Wednesday.
Vitesse Arnhem are a further point back in third spot after a shock 2-0 home defeat by AZ Alkmaar on Tuesday.
Groningen's Serbian-born Filip Kostic became their first player in six years to score at Ajax when he fired home a left-foot effort five minutes before the break.
It brought the visitors level after Ajax, who have now stretched their unbeaten league run to nine matches, opened the scoring with a Lasse Schone penalty in the 27th minute.
PEC Zwolle won 2-1 at 10-man Utrecht with late goals from Denis Mahmudov and Fred Benson in difficult weather conditions to climb to seventh. The home side had Australian Adam Sarota controversially sent off for a high tackle just before the hour.
- Sports & Recreation
- Christian Poulsen
- Twente Enschede