Thanks to their vastly superior goal difference over second-placed Rosenborg Trondheim, who lost 1-0 at Molde on Saturday, a victory against Tromso next week can secure the championship for Stromsgodset.
The leaders had a host of second-half chances against fifth from bottom Start but they took until the 75th minute to break the deadlock, Kovacs nodding in a corner.
The Hungarian also went close to making it 2-0 in the 90th minute.
Rosenborg's title hopes were dealt a serious blow on Saturday when Magne Hoseth converted a penalty 11 minutes from time for champions Molde.
Stromsgodset have 59 points, three ahead of Rosenborg with two games left. Haugesund are third on 48 points.
(Writing by Philip O'Connor; editing by Tony Jimenez)
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