The defeat is the second in a row for Hammarby, meaning Mjallby have the chance to go eight points clear at the top when they face GAIS on Monday evening.
Things began to go wrong for the Stockholm club inside the quarter-hour mark, when Joakim Persson got to the byline and crossed for Isak Bjerkabo, who held off the defender before firing in the opening goal.
The Uppsala side doubled their advantage early in the second half as Persson turned from provider to scorer, as Robbie Ure let Melker Heier's low ball run for the 23-year-old to tap home.
Having played a role in the second, Ure put Sirius in dream land with just over an hour played, latching onto a Leo Walta through ball and powering his strike past the goalkeeper from a tight angle.
Hammarby got themselves a consolation four minutes into added time when Nahir Besara arrowed the ball into the bottom corner from 25 yards, but the damage was done for the Bajen who lose back-to-back league games for the first time this season, while Sirius move 11th with a third win in a row.
Four Allsvenskan matches without a win all but ended AIK's title challenge as they struggled to balance their schedule during their European campain, but having exited continental competition they have returned to winning ways in the league by beating Degerfors 1-0.
The only goal of the game arrived in the 11th minute, when Bersant Celina timed his run into the box expertly to guide Thomas Isherwood's low cross into the bottom corner with his first touch.
AIK created plenty more opportunities, but one goal was enough against hapless Degerfors who have picked up just two points in their last 12 league games.
AIK are 10 points off the top for the time being and remain in fourth place after Malmo were held to a goalless draw at home to IFK Goteborg.
The crucial moment in the match came with just eight minutes to play - a poor challenge by David Kruse on Daniel Tristan Gudjohnsen saw the home side awarded a penalty, only for Elis Bishesari to save Lasse Berg Johnsen's penalty with his foot.
MFF remain third on goal difference, while Goteborg could have overtaken them with a fourth-straight victory, but sit seventh.
Elfsborg are a point further back as they were beaten 2-1 at home to Halmstad - their second defeat in as many games as their title hopes have also faded in recent weeks.
Halmstad were given the perfect chance to score at the perfect time, Emmanuel Yeboah calmly rolled the ball home from the penalty spot in first-half stoppage time to put the visitors in front.
The hosts made four changes at the break and made their last substitution early in the second half, and it paid dividends when Julius Magnusson slammed the ball into the roof of the net with a quarter of the game to play.
But when Pascal Gregor tapped in Villiam Granath's ball across the six-yard box with six minutes to play, Elfsborg had neither the time nor the reinforcements to grab another equaliser. They stay fifth in the standings, while a first win in seven takes Halmstad three points clear of the bottom three.
Despite their dreadful form, Degerfors are being kept off the bottom by Varnamo, who saw their three-match unbeaten streak ended with a comprehensive 5-1 loss to Hacken.
The onslaught began three minutes in when Silas Andersen headed in Samuel Leach's corner, before Isak Brusberg doubled the visitors' lead midway through the half, stretching to tap the ball in following good work from Danilo Al Saed.
Varnamo hit back quickly when Ajdin Zeljkovic's ball across the box picked out Noah Shamoun who finished well, and that's how it stayed until nine minuted into the second half when John Dembe bundled the ball in after two striked had come back off the uprights.
Two Adrian Svanback goals in the final 10 minutes put the icing on the Hacken cake - first he applied a near-post finish when meeting Severin Nioule's cutback, before stabbing home another rebound after Hugo Keto kept out his initial header.
Varnamo stay bottom, three points behind Degerfors and six from a chance of safety, while Hacken climb a place to ninth with their first league win in six matches, as they took have suffered domestically while juggling European football.
Finally on Sunday, Djurgarden continued their recent good form with a 1-0 win at home to Brommapojkarna, taking them to six matches without defeat, yet they stay eighth in the table.
August Priske scored the only goal late in the first half, shrugging off the defence when meeting a long ball over the top and making the finish look easy.
Back-to-back losses keep BP in 10th, five points clear of the bottom three for now.