The striker, who scored twice in the 3-2 EFL Cup defeat to Fulham, netted once in either half, and a first senior goal for Sandro Semedo saw Orient to the victory, while Fraser Franks netted what proved to be a consolation for the visitors who had Dean Wells sent off for an elbow on McCallum after just 13 minutes.
Orient made five changes to the side which lost 2-1 at home to Mansfield Town in the league on Saturday with Sam Sargeant, Callum Kennedy, Robbie Weir, Jordan Bowery and Aron Pollock all coming in.
There was also a maiden appearance in the first-team matchday squad for first-year scholar striker Sam Dalby and second-year scholar attacking midfielder Steven Alzate.
The game was slow to get going but the first chance of the match fell to the visitors and Jake Hyde who from six yards saw his effort well held by Sargeant in the O’s goal.
Opportunities were few and far between but Semedo, playing down the left wing, warmed the hands of former Orient keeper Jamie Jones who gathered the fierce left-footed strike at the second attempt.
It proved to be an unlucky 13th minute for Stevenage’s Dean Wells though who was shown a straight red card by referee Dean Wells for an apparent elbow on O’s striker Paul McCallum.
Semedo was involved on a number of occasions early on, and this time he got on the end of a Harry Cornick cross, taking one touch before firing right-footed, only for Jones to once more gather at the second attempt.
Bowery then found himself one-on-one with Jones, however, the striker’s low effort was saved by the legs of Jones, before being denied by his hands with an effort across goal on 18 minutes.
Following the dismissal it was one-way traffic and Bowery was only able to get the slightest of glances on a pinpoint Nicky Hunt cross as it fell wide of the target.
Chances dried up for a short period of time, however the O’s went closest when a lovely crossfield ball from ball from Kennedy picked out Cornick and from the tightest of angles he struck the post.
But it wasn’t long before the hosts took the lead when on 34 minutes the ball fell to McCallum inside the area following Bowery’s chest down from Cornick’s ball in and ‘P-Mac’ fired home for his third goal in two cup games.
He went close to adding a second just three minutes when he saw an effort fall just over the bar from a Hunt delivery as Orient continued to make the most of the numerical advantage.
The O’s were playing some lovely football, notably through Harry Cornick as he jinked his way superbly between Stevenage defenders before leaving them in his wake and firing an effort which was narrowly off target.
McCallum was on song and he tried his luck with an acrobatic kick three minutes before half time as he got on the end of another pinpoint Hunt delivery, only to see the strike go just over the bar.
Just as the half drew to a close, Cornick went with the outside of his foot with another attempt, this time seeing Jones save well.
Liam Kelly replaced Nigel Atangana at the break for the O’s and was booked within a minute of coming on following protests over a decision from referee Ward.
Just like the first half, the second was slow to get going but it soon became a day Semedo will remember – his first senior goal.
The ball fell to him around eight yards and he volleyed a shot goalwards and with the aid of a slight deflection it found a way past Jones to double Orient’s advantage.
That lead was soon reduced though as five minutes later Fraser Franks rose tallest to head home past an onrushing Sargeant.
A training-ground free-kick almost restored the two-goal cushion though as Callum Kennedy curled an effort wide as Orient remained on top.
It did not take too much longer to double their advantage once more though and Cornick was at the heart of it once more, laying the ball across for McCallum who had the simple job of tapping home.
It was a night of firsts as 16-year-old Dalby made his debut for the club, replacing Bowery with 16 minutes remaining.
Substitute Josh Koroma tried his luck from just outside the box after Kennedy’s corner fell kindly to the youngster as the game began to peter out as it entered its closing stages.
However, Orient had done enough to secure victory on a night which produced a number of positives ahead of their return to league action on Saturday at Morecambe.
ORIENT: Sargeant, Hunt, Pollock, Parkes, Kennedy, Cornick (Koroma 78), Atangana (Kelly 45), Weir, Semedo, McCallum, Bowery (Dalby 74).
SUBS: Cisak, Palmer, Moncur, Alzate.
BOOKED: Kelly (46)
GOALS: McCallum (34, 70), Semedo (54)
STEVENAGE: Jones, Henry (Kerr 77), Franks, Wells, Fox, Pett, Lee, King, Cowans, Hyde (Hunte 59), Godden (Liburd 69).
Subs: Day, Schumacher, Tonge, McKee.
BOOKED: Franks (90)
SENT OFF: Wells (13)
GOALS: Franks (59)
ATTENDANCE: 876 (47 Stevenage fans)
Referee: Gavin Ward