St Mirren v Rangers: Scottish Premiership Sport
Having scored both goals in last weekend's Scottish Cup semi-final win over Hearts, Dessers proved the match-winner again after St Mirren's Mikael Mandron had quickly cancelled out James Bolton's own goal.
It saved nervy Rangers the embarrassment of going four league games without a win for the first time since February 2017.
A sixth straight defeat at the hands of the Ibrox side leaves St Mirren without a win in five games as they remain two points clear of Dundee in their own head-to-head battle for a European place.
The warning signs were there for Rangers as Jack Butland saved twice from Mandron amid an anxious opening eight minutes for the visitors.
Rangers, though, had forced Zach Hemming into three good saves of his own before the goalkeeper flapped at a Borna Barisic delivery and, when Mohamed Diomande headed back across goal, centre-half Bolton knocked it over his own goalline under pressure from Dessers.
However, Mandron outmuscled Leon Balogun at the back post and headed down and in off the far post before Butland brilliantly turned a Bolton volley over the crossbar to deny the hosts a half-time lead.
St Mirren's first goal in six meetings with Rangers left the visitors looking shell-shocked and out of ideas after the break until Dessers rose to head home a Tavernier cross before Butland denied Bolton a second equaliser.