A goal by Adrian Forbes just before the interval sent the Swans soaring back to the top of the table.
In a thrilling encounter, Orient had the chances to take a point back to Brisbane Road but the Swans defence - all at sea against Southend on Saturday - were back to their best and they fully deserved the victory.
Alan Tate and Brad Maylett were the casualties after the weekend's defeat and back into the starting line-up came Andrew Gurney and Forbes.
Orient kept the side that had taken over at the top of the table following their victory over Shrewsbury.
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Minutes later Lee Trundle fired into the back of the visitors net but his effort was disallowed for offside.
The Swans defence appeared a little nervous in the opening quarter and several chances went begging for the visitors.
On the half-hour Trundle turned his man in the area and shot low across Orient keeper Lee Harrison but the ball struck the base of the post before being hacked clear.
In the 37th minute it was Orient's turn to strike the woodwork when a Gary Alexander snap-shot rebounded off the post with Willy Gueret beaten.
The Swans made the breakthrough a minute before the interval when Sam Ricketts slipped a neat pass down the line to Trundle. The man with the golden boots cut inside before crossing to the on-rushing Forbes who side-footed into the empty net.
Forbes sped down the right flank at the start of the second half and his low cross caused panic in the visitor's defence before Donny Barnard cleared to safety.
The Swans were now looking good value for their lead but they had to be careful of the swift breaks out of defence by Alexander and Lee Steele.
Midway through the half Orient brought on a third striker as they went looking for the goal that could keep them on top of the division.
With two minutes remaining a Carlisle free-kick crashed against the woodwork as Orient mounted attack after attack on the home goal but the Swans defence held firm for a deserved victory.