Throwing two points away against rivals Djurgarden last week while Mjallby took another win looked to have all but ended Hammarby's hopes, but a reversal of the top two's results this time has given Bajen some optimism with six rounds of matches to play.
Mjallby looked set for a fourth win with a clean sheet in a row when they went in front just past the half-hour mark - Jeppe Kjaer's corner was met by Axel Noren, whose towering header was perfectly placed past goalkeeper Robin Wallinder.
The home side were given the perfect chance to wrap the game up in the final 15 minutes, courtesy of a foul inside the area by Mattis Adolfsson on Jacob Bergstrom. Elliot Stroud stepped up to take the resulting penalty, but Wallinder got down well to make the save.
That proved crucial just three minutes later when Oster threw bodies forward and Magnus Christensen was on hand to nod home Daniel Ljung's cross and earn the visitors a point which keeps them outside the bottom three and leaves the Hallevik side looking over their shoulder.
That gave Hammarby the chance to respond and cut the lead back down to single digits, which they did in some style by beating Hacken 4-0 in Stockholm.
The home side were made to wait until early in the second half, finding the breakthrough through Tesfaldet Tekie's clean low strike from outside the area.
That opened the floodgates and three minutes later it was 2-0; Paulos Abraham floated through the Hacken defence before teeing up Nahir Besara to stroke the ball into the bottom corner.
It only took five more minutes for the next to arrive, as Abraham turned from provider to scorer, getting on the end of Hampus Skoglund's cross to apply the simple finish from close range.
20 minutes from time, Skoglund drove into the box himself and looked to have been brought down, but the loose ball was picked up by the alert Montader Madjed, who took it around the goalkeeper and slotted number four into the empty net.
Since their back-to-back losses last month, Hammarby have matched Mjallby's seven points from a possible nine. Hacken's form has dipped severely, they are now on a three-match losing run and in danger of being dragged into the relegation battle.
Hacken are four points clear of the bottom three but now just seven points clear of the two automatic relegation places after Degerfors picked up their first league win since 15th May, ending their 14-match winless run by beating Sirius 3-1 away from home.
It looked to be business as usual for the strugglers when Leo Walta put the hosts in front from the penalty spot inside 20 minutes, but Degerfors tied things up before the hour mark when Marcus Rafferty curled a peach into the top corner.
The unthinkable happened in the 91st minute - Santeri Haarala won possession in the Sirius half and played the ball forward to Dijan Vukojevic, who took aim from the edge of the box and powered Degerfors into the lead.
And almost from the restart, the visitors won the ball again and made it a trio of sweet strikes as Philippe Ndinga drilled an effort with his left foot from 25 yards in off the post to seal the three points.
With four wins in their previous five, the result comes as a real surprise for Sirius, who remain 10th, the best-placed of three sides who are four points clear of the bottom three.
An Ezekiel Alladoh goal decided Sunday's other match, as Brommapojkarna picked up all three points on the road against Goteborg, ending IFK's six-match unbeaten run in the league.
That meant Goteborg failed to regain fourth place, instead losing it to Gamla Ullevi rivals GAIS, who ran out 2-0 winners over 10-man Elfsborg on Saturday thanks to strikes from Robin Frej and Rasmus Niklasson, with both goals arriving late in either half.
Having left it late to draw with Hammarby last week, Djurgarden did the same to take victory on the road in Malmo, as August Priske hit an 88th-minute winner.
That result leaves Malmo in sixth and without a win in four, and more importantly, 18 points behind Mjallby with only 18 left to play for. Djurgarden, meanwhile, sit just a point behind in seventh having put together a nine-match unbeaten run.