Hammarby were smelling blood after their fellow title-chasers Hacken took Sirius apart two nights earlier, and they made sure to take advantage with a third win in a row, while it's successive defeats for GAIS back in 10th place.
The home side's eagerness was epitomised by their two goals arriving in the first 11 minutes - Victor Lind broke the deadlock when his initial first-time hit was blocked, but he latched onto the rebound, made space for himself and fired into the bottom corner.
And five minutes later, Lind turned provider when he intercepted a sloppy pass across GAIS' own penalty area, and as the goalkeeper attempted to close him down, he squared to Paulos Abraham, who found the empty net despite the despairing attempts to block by defenders.
In the second half, Warner Hahn had to be alert to tip a Nikola Vasic strike around the post, before Lind and Abraham both went close to completing braces late on, but victory for Hammarby was secured.
Hammarby's gap to those outside the European places is now eight points after Elfsborg moved into fourth but only by picking up a point at Goteborg, who remain in 12th place.
Following a goalless first half, the home side went ahead just after the hour mark, as Julius Beck was adjudged to have fouled Felix Eriksson in the box, and Sam Larsson sent the goalkeeper the wrong way from the penalty spot.
But in the 90th minute, Goteborg were denied a third win in four when an attempted through ball deflected kindly into the path of Leo Ostman inside the area, and he got his shot away despite plenty of blue and white shirts around him to rescue a point for the Boras side.
Elfsborg are unbeaten in four despite their three-game winning run ending, and sit above AIK on goal difference and three points clear of Hacken.
Two late goals won Brommapojkarna the points at home to Degerfors, sealing a second win in a row as they extend their unbeaten run to three, while the visitors remain in the relegation play-off place with a first loss in three.
The key moment arrived 10 minutes from time, when Mads Hansen was upended inside the area by Samba Diatara, and Hansen dusted himself off to send his penalty straight down the middle and give BP the lead.
Soon after, the points were secured when Anton Kurochkin burst through the middle, and despite having options either side, decided to go for goal himself and picked out the bottom corner with a curling effort from almost 30 yards.
The Bromma Boys are up to ninth in the standings, while Degerfors are three points shy of Kalmar and two clear of Orgryte.
That gap between Degerfors and Kalmar has grown to three as Roda Broder picked up a point in a goalless draw at Vasteras. The visitors had the majority of the efforts on goal but the only big chance of the game was passed up by Vasteras' Mamadou Diagne, who blasted over from six yards out when unmarked. The home side remain in eighth place and are two without a win, while Kalmar haven't won in four matches.