Kenny Jackett named an unchanged side from the team that played against midweek against QPR, with striker Harry Smith named on the substitutes bench for the first time.
Orient took an early lead which set the home crowd bouncing, with that man Aaron Drinan doubling his tally for the season.
After good pressure, the ball was worked back into the box by Archibald, finding the onrushing Drinan with just the keeper to beat.
He did just that, with his half volley giving Dawson little chance from close range, and The O’s found themselves ahead.
Then, with twenty five minutes on the clock, things got better for The O’s, as Omar Beckles once again showed he knows exactly where the net is.
Tom James’ free-kick found the flick from Dan Happe, who, turning provider for the second time, picked out his defensive partner.
Beckles was there to meet the knock down, stay strong against his marker, and sneak it past Dawson to double the lead.
And it could have been three not long after, with some wonderful football from The O’s opening up the Grecians once again.
Drinan and Archibald combined first, playing in Kemp – who opened up to deliver the ball to Sotiriou.
Sotiriou was blocked off close range from Sweeney, with the ball turned agonisingly over the bar from the defender.
The visitor’s had their first meaningful sight of goal with five minutes to go in the half, and really should have made Orient pay.
Sparkes worked his way into the box, feinted an effort which saw him afforded acres of space – but his instinct not to shoot cost him, and Orient cleared.
After the break, the hosts started brightly, and looked the most likely to nick the next goal.
And the pressure began to tell when Jevani Brown’s touch saw him take it away from Vigouroux, who in turn bought the Exeter man down.
Matt Jay stood up to take the penalty, but unlike the reverse fixture last season, Lawrence Vigouroux pulled off the save, and keeping the two goal lead in tact.
Soon after, the misery was compounded for Exeter, when Jonathan Grounds was given his marching orders for a second yellow card – with fifteen minutes still to play.
It didn’t take long for Orient to capitalise, and in a wonderfully worked move, Aaron Drinan’s cross into the box was masterfully converted by Theo Archibald, for his first goal in red – and to secure the three points.
The goal was a well worked move that began all the way from the goalkeeper, and showed another side to the hard working Orient side that had drawn the first two games.
The O’s were in cruise control from here on in, and despite a late chance for Pierce Sweeney in the box – saw out a comfortable first win under Kenny Jackett.
Leyton Orient: Vigouroux, James, Wood (Sweeney 82′), Happe, Kemp, Archibald, Drinan, Pratley ©, Beckles, Sotiriou (Smith 67′), Kyprianou.
Subs: Sargeant, Clay, Smith, Young, Sweeney, Ogie, Tanga.
Goals: Drinan 7’, Beckles 35’
Exeter City: Dawson, Sparkes (Rowe 62′), Ataganga, Ray, Jay © (Amond 70′), Seymour, Key, Dieng (Kite 46′), Brown, Sweeney, Grounds.
Subs: Lee, Caprice, Amond, Rowe, Dyer, Kite, Dodd.
Red cards: Grounds
Penalty miss; Jay 65′