Mallinder stepped up with two minutes to go to land a penalty that ensured Exeter Chiefs would suffer a 20-19 defeat at Franklin’s Gardens.
Saints, who had already suffered defeats to Bath at Wasps on home turf, were 13-0 down inside just 13 minutes.
But George North’s try and brilliant run to set up Rory Hutchinson, allied with two Mallinder conversions, sent Saints in 14-13 up at the break.
Gareth Steenson landed two penalties to put Exeter back in control, but Mallinder’s penalty double ensured it would be Jim Mallinder’s men who celebrated a crucial win.
Mallinder had been forced to move to 10 before the game as Stephen Myler pulled out with an arm injury.
That saw Scotland Under 20s centre Hutchinson come in for his first Saints start as he took Mallinder’s place at 12, with Sam Olver on the bench.
But it was all Exeter in the early exchanges and after the forwards won a penalty with a drive, Steenson booted the away side into the lead.
And the dominance continued as some patient build-up play eventually saw Henry Slade and Ollie Devoto combine superbly to set Olly Woodburn free in the corner.
Steenson added the extras to put Exeter 10-0 up with just 10 minutes gone and it was soon 13-0 as the fly-half slotted a second penalty.
Saints hadn’t got going at all and even when a chance came their way, they wasted it as Nic Groom knocked on a Louis Picamoles pass with men waiting to race in for the score.
But the home fans finally had something to shout about on 25 minutes as George Pisi offloaded and Picamoles powered forward before North forced his way over the line.
Mallinder landed the conversion with aplomb and, in the blink of an eye, Saints were ahead, with North again at his blistering best.
The Wales wing broke clear, dancing around attempted tackles before feeding Nic Groom, who put Hutchinson in for a score to remember.
Mallinder converted to make it 14-13 to the home side and things were going Saints’ way as Steenson missed a simple penalty chance.
Confidence was suddenly flowing through Saints veins as displayed by Mallinder, whose ambitious drop goal attempt drifted just wide.
The home side headed in at half-time a point up and they started strongly in the second period, with the tempo still high.
But Steenson put Exeter back in front with a penalty in the 54th minute and the sting hhad been taken out of Saints.
Another Steenson effort from the tee made it 19-14 to the away side with just 14 minutes of the match remaining.
But Mallinder replied with a calm and collected penalty to bring his side back to two behind heading into the final 10 minutes.
Tension levels were rising and Saints needed to summon one final push.
They did, putting pressure on Exeter and forcing referee Matt Carley to award a penalty.
Mallinder was the young man charged with a big kick that would put Saints in front, and he stepped up to calmly edge it between the posts.
Now there were two minutes left for Exeter to save the game, but Saints won a crucial penalty and eventually Picamoles booted the ball out to bring a huge roar from the home fans.
Saints: Foden (c) (Olver 68); K Pisi, G Pisi (Tuala 61), Hutchinson, North; Myler, Groom (Kessell 63); A Waller (Ma’afu 63), Haywood, Brookes (Hill 57); Lawes, Paterson (Dickinson 70); Gibson, Clark (Harrison 58), Picamoles.
Exeter Chiefs: Turner; Woodburn, Devoto, Slade, Whitten (Nowell 56); Steenson, Chudley; Moon (Hepburn 48), Yeandle (c) (Cowan-Dickie 48), Holmes (Williams 60); Lees (Welch 58), Parling; Dennis, Horstmann, Waldrom (White 78).
Referee: Matthew Carley