Rovers were the main aggressors throughout the match but it did not look like being their day until 12 minutes from time when Gresko's speculative shot bounced into the far corner courtesy of a huge deflection off Stephen Carr's back.
A drab first half saw few chances for either side although it was the hosts that just about shaded things with Dwight Yorke going close with a header while Andy Todd had the best chance of the half when he fluffed his header from Brett Emerton's corner when completely unmarked.
Graeme Souness was then sent to the stands by referee Graham Poll after seven minutes of the second half after the fiery Scotsman had a furious argument with the fourth official and he was asked to leave the touchline by the match official.
Souness nearly missed Spurs go close to opening the scoring while he was still climbing up into the stands, as Mauricio Taricco's cross found Helder Postiga free in the box but his volley went over.
Yorke had another golden opportunity on 65 minutes when he flew in at the near post from Emerton's cross but although he got there in front of Kasey Keller the ball was somehow bundled wide.
Robbie Keane blazed over left footed on the counter attack but Rovers were looking the more threatening in attack, and Keller had to be alert to produce a smart save to tip Yorke's downward header round the post.
Rovers were piling forward but looked like drawing a blank until Gresko broke the deadlock, with the help of a huge slice of luck.
The Slovakian defender powered forward towards the Spurs box and tried his luck from 25 yards out and, although his effort looked a bit speculative, it took a wicked deflection off Carr that totally deceived Keller and spun into the far corner.
Gresko's first goal in English football gave Rovers a vital three points in their fight to get away from trouble at the foot of the table.
