The visitors took the lead through Steve Guppy after the break and looked to be in control of the game, and only some fine goalkeeping from Martin Rice prevented Borough stretching the lead.
But with three minutes left on the clock Jones floated in a free-kick from 35 yards which deceived the goalkeeper and drifted into the top corner off the underside of the bar.
A draw was probably a fair result, although rapidly-improving Stevenage will feel robbed of an unlikely maximum.
Exeter were lively in the opening stages and stand in skipper Lee Phillips could have given them the lead inside two minutes.
The forward ran powerfully into the box after picking up a loose ball in midfield and shot a foot wide from 15 yards.
Stevenage also looked a threat going forward. Craig Dobson's cross was cushioned by Ronnie Henry and striker George Boyd struck a left foot shot into the arms of the goalkeeper.
Much of the first half was scrappy, but Stevenage could have opened the scoring just before the break.
Steve Morison burst through the City defence and as he prepared to shoot from 12 yards the striker was robbed by a superb recovering tackle from Jon Richardson.
After the interval Exeter were more positive. Richardson bravely leapt to meet Andy Taylor's deep cross and was unlucky to head wide under pressure from the goalkeeper.
Phillips then showed what he his capable of when he rifled a fierce shot over the bar after twisting and turning inside the box.
But Stevenage regularly threatened to grab a goal. Craig Dobson struck the bar after Morison's shot was half cleared, before the visitors finally took the lead just before the hour mark.
Morison drilled the ball across the face of goal and Guppy scored his first goal for Stevenage with a low shot from a tight angle.
The goal stunned Exeter but it was no more than Stevenage deserved. They continued to hit Exeter on the break and Morison struck the ball over the bar after being put clean through on goal.
Morison could easily have had a hat-trick. He headed well from Dobson's fine cross and was denied by a superb save from Rice.
Exeter desperately chased the game and Dean Moxey fired the ball into the arms of the goalkeeper from the edge of the box. Phillips then came within inches of a leveller when he beat two defenders inside the box and struck a low shot agonisingly past the post, with the goalkeeper beaten.
With three minutes left Jones floated in a free-kick which appeared to be over-hit but dipped in time to sneak in off the underside of the bar to the delight of the home fans.