Sam Stubbs scored twice in 15 minutes as City took all three points at a sun-drenched and packed St James Park.
The centre-back celebrated his first goal for City in the 29th minute as a pin-point delivery from Jevani Brown found the head of the centre back, whose effort flew past the gloves of the opposition keeper.
The opposition found the equaliser in the 10 minutes later as Elliot List’s cross found Luke Norris at the far-post who poked home from close range.
But a minute before the break, Stubbs doubled his and City's tally, following another Jevani corner sealing the points for the Grecians, with neither side able to net in the second half.
Matt Taylor made two changes from Tuesday’s goalless draw with Callum Rowe being given his first home league start off the back of an impressive away performance at Port Vale.
The first chance came for the hosts in the fifth minute as some steady play down the left-hand side allowed Jack Sparkes to deliver a teasing cross just missing the head of skipper Matt Jay.
Sparkes continued to cause problems for the visitors as his second threatening cross of the afternoon, this time found the head of MJ who was only able to steer inches over the cross bar.
The 27th minute saw Josh Key threaten with a low effort towards the bottom left corner, but the outstretched hand of former Grecian Christy Pym pushed the ball off the pitch to safety.
The resulting corner was whipped in promisingly from the in-form Jevani Brown and defender Sam Stubbs connected emphatically with his head to bulge the back on the Stevenage net for his first City goal.
The lead didn't last long as in the 38th minute Stevenage seriously threatened City for this first time. Elliott List’s low cross from the left rolled through the box and found the grateful foot of striker Luke Norris who poked home the equaliser for the visitors.
Despite the setback, City continued to press Stevenage down the right side, winning a corner in the 44th minute on the same side.
Another impressive delivery from Jevani once again found the towering head of Stubbs who produced another bullet header towards the centre of the goal which passed the helpless gloves of Pym, doubling his goal tally on the day.
City continued to press home their advantage at the start of the second half as the Grecians looked to extend their half time lead.
A long searching throw from Alex Hartridge found its way to Brown in the centre of the box, whose quick turn allowed the striker to fire at goal, but unfortunately for City unable to find the goal.
A glorious opportunity presented itself to MJ in the 54th minute as Jevani outmuscled his defender to play it into the path of the skipper, whose shot dragged wide of the left post.
City were starting to dominate possession with Stevenage struggling to find solutions to the slick passing of their opponents.
A quiet period followed with both teams trying to make the most of the half chances presented.
The best efforts of Stevenage resulted in a cross from the right side finding the head of substitute Bruno Andrade who could only lift the ball over the bar.
With 15 minutes left of the match, there was little to separate the two sides as the home fans tried their best to push the Grecians home for a third.
A great chance for the City came in the 78th minute for Offrande Zanzala as he broke away from the Stevenage back line, but a tame effort was easy to deal with for Pym.
After a long spell of possession for City, Stevenage took their chance to brake forward down the left-hand side as Andrade’s effort required Dawson to produce a strong hand to deal with the danger.
City looked set to make it a third in the closing moments as a quick charge forward fell to Josh Key who failed to capitalise on a great chance.
Exeter City: Dawson, Key, Sweeney, Hartridge, Stubbs, Sparkes, Collins, Rowe, Jay © (Coley 84’), Brown, Zanzala (Phillips 80’)
Subs: S.Brown, Diabate, Caprice, Dieng, Coley, Phillips, Amond
Stevenage: Pym, Coker, Cuthbert ©, Prosser, List (Reid 69’), Taylor, Norris, Carter, Westbrooke (Andrade 59’), Vancooten, Barry
Subs: Walker, Andrade, Lines, Upson, O‘Neil, Read, Reid
Referee: Carl Boyeson
Attendance: 5,923 (89 away)