Fletcher made one change from the mid-week defeat away at Plymouth Argyle with George Marsh replacing Dale Gorman. On the bench, Myles Judd returned taking the place of Hector Kyprianou.
Orient started the game brightly and they had an early penalty appeal turned away after James Brophy went down in the box in the fourth minute.
However, referee David Rock, was left with no choice but to point to the spot two minutes later, after Brophy again went down following a clumsy challenge from Jarrad Branthwaite.
Josh Wright stepped up and coolly slotted past Adam Collin in the Carlisle goal to net his sixth goal of the season and give the O’s an early lead.
Orient continued their fine start throughout the early stages and some great interplay between Joe Widdowson and Brophy led to the latter finding Matt Harrold in the box, but his effort was well turned away by Collin.
From the resulting corner, the O’s almost added a second when Marvin Ekpiteta was foiled in his attempt to scramble home before Josh Coulson hit a shot wide on the turn.
Harrold had another opportunity in the 25th minute when he was found in the penalty area by Craig Clay, but he was crowded out by the Carlisle defenders as he tried to get a shot away.
The away side struggled to get a foothold in the game throughout the first half, and it wasn’t until the 39th minute that they had their first shot in anger. However, Mike Jones’ effort was comfortably held by Dean Brill.
Carlisle manager, Steven Pressley made a change at the break bringing on Olufela Olomola for Jarrad Branthwaite, which saw them switch from a back three to a back four.
This switch had an immediate impact as just two minutes after the restart his side were level. Jack Iredale scrambled the ball home from Jack Bridge’s corner to restore parity for his side against the run of play.
Carlisle looked a different team in the second half maintaining their fast start throughout the opening 15 minutes of the second period, and in an attempt to stem the tide Fletcher brought on Jordan Maguire-Drew in place of James Dayton.
Ten minutes later, the O’s Head Coach made another switch this time Matt Harrold came off the field to be replaced by Louis Dennis.
Orient struggled to regain their first half dominance and with ten minutes remaining Fletcher rolled the dice for the final time with Dale Gorman coming on for George Marsh in central midfield.
The O’s’ best chance of the second half fell to Brophy, who after being played in by Clay, was denied by a wonderful save from Collin in the 84th minute.
Carlisle followed that up immediately with a good chance of their own, when substitute Olufela Olomola sprang the offside trap but his effort was denied by the legs of Brill, in what was his 100th appearance for the club.
Deep into stoppage time the O’s had a chance to win it, however Gorman failed to keep his shot down and Orient had to settle for a point in Fletcher’s first home game at the helm.
ORIENT: Brill, Ekpiteta, Coulson, Happe, Widdowson, Clay, Marsh (Gorman 83″), Wright, Dayton (Maguire-Drew 63”), Brophy, Harrold (Dennis 72”)
SUBS: Sargeant, Judd, Turley, Alabi
GOALS: Wright 7”
CARLISLE: Collin, Iredale, Mellish, Thomas (Hope 83″), Jones, McKirdy, Jones, Webster, Bridge, Branthwaite (Olomola 46″), Sagaf (Knight-Percival 87″)
SUBS: Gray, Elliot, Scougall, Sorensen
BOOKED: Sagaf 28”, Thomas 69”, Webster 79”
GOALS: Iredale 47”
REF: David Rock
ATT: 5,765 (552)