The visitors meanwhile sit in 13th, but they know that a win could see them climb as high as seventh if other results go their way and they do have a game in hand on a number of teams above them in the table.
Match preview
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Leyton Orient come into this game on the back of an impressive display against promotion hopefuls Wrexham on Saturday, when they held the away side to a 0-0 draw at Brisbane Road.
The Os had more possession and created the better chances in the game, and manager Richie Wellens will have been delighted to see his side extend their unbeaten run to four games while giving such a good account of themselves.
Their upturn in form is all the more impressive considering their start to the season, although the Os are now winless in their last six home outings.
Leyton Orient have also been very impressive in September, coming away with a 2-2 home draw against Peterborough United and a 4-1 away win at Stockport County in recent outings, so they have proven that they are able to cut it among the top sides in the division.
Things do not get much easier in October though, with trips to Lincoln City and Wycombe Wanderers waiting for them, as well as a home game against Huddersfield Town, so a win on Tuesday evening could set them up nicely for a tough run of upcoming fixtures.
Exeter also come into the Leyton Orient game on the back of a 0-0 draw, with theirs being a somewhat fortuitous result away at Wigan Athletic as they did not muster a shot on target and were thankful for the wastefulness of the Latics.
That is not where the similarities end with Tuesday's opponents though, as Exeter have also had a strong September, with league victories over Swindon Town and Stevenage, and an EFL Trophy win against Tottenham Hotspur Under-21s.
The Grecians currently sit in mid-table but their recent results and clean sheets against Wrexham, Bolton Wanderers and Rotherham United could have fans hoping for a finish in the top half or even a potential push for the playoffs if they can find some consistency.
Manager Gary Caldwell led Exeter to a 13th-place finish last season with 61 points from their 46 games, but in the early stages of a new campaign, it remains to be seen whether or not they can progress up the table in the 2024-25 season.
There have not been many goals in games involving Exeter this season though, as they have only scored eight league goals and conceded just six, with this midweek game being potentially another low-scoring affair.
Leyton Orient League One form:
L
L
W
W
D
D
Leyton Orient form (all competitions):
L
W
L
W
D
D
Exeter City League One form:
L
L
W
L
W
D
Exeter City form (all competitions):
W
W
L
W
W
D
Team News
The Leyton Orient team could largely resemble the same one that started and played so well against Wrexham, although Jamie Donley could start in attack alongside Charlie Kelman, with Sonny Perkins also on standby to lead the line.
Captain Darren Pratley could return if the manager opts to add some experience to his starting XI, otherwise Dominic Ball and Sean Clare could keep their place in the centre of the park.
Meanwhile for Exeter, Omar Beckles, Brandon Cooper and Jack Simpson are once again likely to compose of the back three that has been defensively solid so far this season, and goalkeeper Zach Hemming has also played a big part in this strong record.
For Exeter, Yanic Wildschut is a long-term absentee after the forward was ruled out for the season with a knee injury, and fellow winger Patrick Jones is also expected to miss out here.
However, with the recent return of Sonny Cox, Wellens still has a strong squad to pick from for the trip to Leyton Orient and he could keep with a similar side that played on Saturday, although Jay Bird could push for a start alongside Josh Magennis in attack.
Leyton Orient possible starting lineup:
Hemming; Beckles, Cooper, Simpson; James, Ball, Clare, Currie; Donley, Donley, Kelman
Exeter City possible starting lineup:
Whitworth; Sweeney, Crama, Yfeko; McMillan, Francis, Woods, Aitchison, Niskanen; Bird, Magennis
We say: Leyton Orient 1-1 Exeter City
Leyton Orien's recent upturn in form has seen them climb out of the relegation zone in recent weeks, and while they are on a good mini run, they are now winless in their last six home games.