Less than a week on from replacing Miguel Angel Ramirez in the Malmo dugout, Helstrup saw his side secure all three points at Degerfors - a second win in a row since the Spaniard departed.
Chances were at a premium in the first half, and the home side were frustrated by the concession of a simple goal early in the second. A deep corner to the back post was prodded back across goal by Kenan Busuladzic for Erik Botheim to force home from inside the six-yard box.
Degerfors then didn't do enough to get back on level terms - a Samba Diatara corner in added time almost flew all the way in, but tipping it around his post was the only time Robin Olsen was really stretched.
Malmo climb to sixth place, while no wins in seven keeps Degerfors hovering above the bottom three.
Three places but just one point behind Malmo are Vasteras, who kept pace with the record Swedish champions thanks to a victory over Halmstad, one of three sides who Degerfors can still look down on.
The afternoon could not have begun better for Halmstad, who took the lead with exactly a minute played. An early corner was played by Joel Allansson to the edge of the area, where Hussein Carneil was waiting to unleash a sweet volley that flew into the net.
But the good times for the hosts lasted all of three minutes, when Vasteras won a corner of their own, which Ismet Lushaku swung in to the near post where Mikkel Ladefoged was waiting to nod in. Midway through the first half, Vasteras went ahead when Ladefoged turned provider, poking a pass on to Taonsa Axel, who jinked past the HBK defence before slotting into the bottom corner.
A route back into the contest was made less likely for the hosts soon after, when Andreas Boman brought Taonsa down outside the box, a challenge the referee deemed to have denied a goalscoring opportunity, and the red card was brandished.
Vasteras made the man-advantage count just past the hour, when Taonsa met a Ladefoged cutback and his shot had too much power for goalkeeper Tim Ronning, who was then guilty of bringing down Mamadou Diagne inside the area, only to spoil a perfect afternoon for Ladefoged by saving his penalty with his feet.
It's two wins in three for Vasteras either side of the break, while Halmstad stay off the bottom on goal difference after successive losses.