A win for Mjallby tomorrow against IFK Goteborg will get them over the line, but with victory in the Stockholm derby, Hammarby are dragging it out as long as possible.
The home side made the breakthrough against AIK with five minutes of the first half to play, when Montader Madjed clipped in a cross from the right side of the area, which Nahir Besara flicked into the bottom corner of the net.
Just before the hour mark, Bajen were in control - Adrian Lahdo won the ball back on the halfway line and drove forward to the edge of the area. He squared the ball to Madjed, whose strike towards the near post had too much on it for Kristoffer Nordfeldt in the AIK goal.
Approaching the final 10 minutes, Aron Csongvai curled in a 25-yard free-kick to give the Solna side hope.
One more goal for the visitors would leave Mjallby needing just a point tomorrow, but Hammarby held on for a 2-1 win, meaning only victory can give the team from Hallevik their crowning moment in this round of fixtures.
While Hammarby have picked up momentum, AIK are fading fast - with no wins in their last four, they have dropped to fifth and are at risk of missing out on European football for next year.
Sitting in third place, four points clear of AIK, are GAIS, who held off Djurgarden 3-2 to extend their unbeaten run to four matches and end the visitors' 11-match unbeaten run in the league.
Ibrahim Diabate got the Gothenburg side off to a strong start with a quarter of an hour played, chesting down a ball into the box and applying a firm finish.
Eight minutes later it was 2-0, as the Mackerels launched a superb counter-attack from inside their own half, and no one in blue could stop Amin Boudri, who went clean through on goal and delicately lofted the ball over the advancing Filip Manojlovic.
August Priske beat the offside trap and finished well to reduce the deficit 10 minutes before the break, only for Robin Frej to restore the two-goal cushion just before the hour mark with a close-range header.
With 20 minutes to play, the Iron Stoves got back in the game again thanks to a one-time finish into the roof of the net from Mikael Anderson, but GAIS held on for back-to-back wins and condemn Djurgarden to a first loss since 13th July.
Also on Sunday, Elfsborg put their dreadful recent form behind them by thrashing Oster 5-1. That result, coupled with Varnamo's 1-1 draw with Brommapojkarna, keeps Varnamo's survival bid alive by the skin of its teeth.
Things looked bleak for Varnamo when Oscar Uddenas gave Oster an early lead against the side who were eight without a league win before today. But two Taylor Silverholt goals quickly turned things around for Elfsborg.
Strikes from Arber Zeneli and Ibrahim Buhari in the first 10 minutes of the second half all but sealed a rare victory for the Boras side, before Per Frick completed the rout in stoppage time. Elfsborg stay in eighth place, while Oster stay in the Relegation Playoff place, three points behind Halmstad.
A shock win over AIK last time had kept Varnamo alive, and a late leveller this afternoon has maintained their Allsvenskan status for now. They are eight points behind Oster with three matches to play, but should Degerfors beat Halmstad tomorrow, it will all be over for the Jonkoping County side.
Victor Lind's header for BP six minutes from time this afternoon looked to have sent Varnamo to the Superettan, only for Marcus Antonsson to equalise in the 90th minute to keep them fighting for another day.
On Saturday, Malmo picked up their second win under Anes Mravac and moved into fourth place with a 2-0 win over Norrkoping, thanks to a goal in each half from Emmanuel Ekong and Hugo Bolin.
The victory keeps MFF three points shy of GAIS, who have the same goal difference. Norrkoping sit 12th after three successive defeats and are not safe yet, sitting four points from the Relegation Playoff place.
Within touching distance of safety are Hacken and Sirius after they drew 1-1 in Gothenburg yesterday to move eight and five points clear of the bottom three, respectively.
Mikkel Rygaard gave the home side the lead after 16 minutes, but Isak Bjerkebo levelled for Sirius on the stroke of half-time.
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