Having won a top-of-the-table clash with Mjallby at the weekend, AIK were full of confidence ahead of their trip to Gothenburg, and that confidence translated into scoring the opener 16 minutes in, when Benjamin Tiedemann nodded in Bersant Celina's corner at the near post.
But Hacken were in no mood to lie down and, just before the hour mark, equalised when Leach took aim from 30 yards and picked out the top corner in stunning style.
Four minutes on, an upset was on the cards when the Getingarna went in front - Severin Nioule set up John Dembe and after his strike was saved, Nioule followed up and finished well on the rebound.
Soon after, the match swung back AIK's way with two goals in even quicker time. First, a Mads Thychosen cutback found Victor Andersson waiting just inside the box to sweep the ball into the top corner.
Within three minutes, AIK were back in front - after winning the ball high up the pitch, the ball was worked across to Andronikos Kakoullis, who applied the simplest of finishes past the stranded Etrit Berisha in the Hacken goal.
Just when the Gnaget thought they were home and dry, there was to be one final twist - in added time, Ben Engdahl got to the byline and pulled the ball back to the arriving Leach, who curled the ball across goal and into the opposite corner for his second top quality goal of the match to share the spoils.
The 3-3 draw keeps AIK unbeaten but they have now dropped points in their last two away trips. Despite the positive ending, it's only two wins in eight for Hacken.
AIK's slip-up was capitalised upon by Hammarby, who moved within a point of the leaders by winning a topsy-turvy game of their own at home to Sirius, 3-2.
After a slow start to the campaign, Sirius arrived at the 3Arena unbeaten in three, and gave themselves a solid chance of making it four when they took the lead after five minutes. A half-cleared corner was chested down Tobias Carlsson into the path of Noel Milleskog, who rifled the ball in off the post.
The lead only last six minutes as, from a corner of their own, Victor Eriksson headed home at the near post. Then Hammarby were in front 10 minutes after half-time when Sirius failed to clear a low cross into their six-yard box and Nahir Besara was on hand to apply the finish when the ball fell his way.
Going behind brought out the best in the visitors, and they were deservedly level with a quarter of the match remaining thanks to Melker Heier winning the ball in a dangerous area and finding Robbie Ure, who scored his second goal in any many matches.
But the Uppsala side could not hang on, falling behind just three minutes later when Abdelrahman Boudah glanced home Jacob Ortmark's cross.
AIK welcome Hammarby to Strawberry Arena on Sunday for what could be another first-versus-second clash for the hosts in as many weekends, depending on Mjallby's result tonight against Djurgarden.
Last night's other fixture saw draw specialists GAIS win for the first time in six outings, moving up to sixth for the time being, as an Ibrahim Diabate hattrick downed Halmstad, 3-1.
The home side's Yannick Agnero scored for the fifth match in succession to give the hosts the lead.
But Halmstad had no answer to Agnero's Ivorian compatriot Diabate, who nodded in an equaliser midway through the first half, skipped past the goalkeeper and bundled the ball home soon after half-time, and buried a powerful low strike into the bottom corner inside the last 10 minutes.
Halmstad stay just outside the bottom three after their two-match winning run came to an end.
Follow tonight's five remaining Allsvenskan Round 9 fixtures on Flashscore.
