A goal in each half from Ruel Sotiriou capped off a brilliant display by the forward, whilst Happe and Kemp also found the net in alternating halves.
Kenny Jackett made seven changes from the defeat at Vale Park at the weekend, with Antony Papadopoulos returning to the side after his match winner in this competition last time out.
And it was a positive start to the game for the bright yellow O’s, with Ruel Sotiriou finding the net after just seven minutes.
It was an instinctive finish from the forward, who capitalised on a deflection with a wonderful touch, before rifling a half volley off of the post and into the net.
This gave The O’s a sense of confidence, and they continued the game in this form, with Dan Happe soon doubling the lead with a well-taken goal.
The O’s nearly doubled their lead quite soon after through an unlikely source, as Antony Papadopoulos’ cut back found Jayden Sweeney in the penalty box, but his strike was blocked by Tony Craig.
It came from a fantastic delivery from Tom James, who found Happe towering inside the six-yard box – and the centre-back guided his header past Dion-Curtis Henry.
Tyrese Omotoye was keen to add to the scoresheet, working hard to win the ball back – but on the two occasions he found a sight of goal, his low efforts were well saved by Henry.
Crawley threatened on occasion, Khaleel wrapping one wide of the post, but The O’s were two to the good at the break.
Whilst Crawley started the second half better of the sides, it wasn’t long until Leyton Orient furthered the deficit – Ruel Sotiriou again the liveliest in the penalty box.
A long throw from Shad Ogie was poorly defended by the Town contingent, and it fell to Sotiriou with time and space, who thumped a powerful half-volley home.
Tom James, known for his free-kick scoring ability in his career, gave everyone a glimpse of what he can do with a set-piece with a powerful effort dipping just over the bar.
But soon enough Orient did have their fourth, as a well worked move saw room open up for Craig Clay, who, playing in right-wing back, picked out Hector Kyprianou, who supplied a great cross into the box.
This fell into the path of Dan Kemp, who made no mistake from inside the six-yard box.
This capped off a brilliant team performance for Orient, with Charlton Athletic next up to determine the winner of Group H.
Crawley Town: Henry,Davies, Gallacher, Craig, Dallison, Powell, Battle, Tilley (Frost 60′), Khaleel (Appiah 61′), Bansal-McNulty (Kevser-Junior 85′), Marshall.
Subs unused: Morris, Francomb, Rodari, Hessenthaler.
Leyton Orient: Byrne, James, Happe, Clay, Kemp, Omotoye (Nkrumah 79′), Sotiriou, Papadopoulos, Sweeney, Ogie, Kyprianou.
Subs unused: Wood, Archibald, Drinan, Beckles, Young, Vigouroux.
Goals: Sotirou (2), Happe, Kemp.
Attendance: 810 (106 away)