When Kelman headed in his 15th league goal of the season to put Orient ahead, it appeared to be the first step on the ladder towards a comfortable midweek victory.
But by half-time the hosts had lost their footing. The first half had worn on to a game of few chances but with the visitors beginning to get players forward and time on the ball.
And the Boro were well on top for most of the second half, with Dan Kemp unable to take advantage of a poor backpass from Clare before Brandon Hanlan volleyed wide and Jamie Reid fired into the side netting.
Keeley, so often the hero for the O's, was forced into two big saves, firstly from White from close range in the 90th minute, before diving low to his right to deny List in added time and help secure the Orient's second win in a row.
A superb run of 12 wins in 15 matches either side of Christmas had Richie Wellens' O's sitting sixth in the table.
But five defeats on the bounce saw them tumble out of the top six as their season threatened to peter out.
However, they have once again bounced back by taking maximum points away at Blackpool and then Stevenage to move two points behind sixth-placed Huddersfield Town.
Orient will face teams currently in the bottom half of the table in five of their next six matches with a chance to make further ground back on their rivals before hosting automatic promotion chasers Wycombe and a mouthwatering visit to Huddersfield on the final day of the season.
