Orient came from behind to ease their relegation worries, but in doing so piled the pressure on struggling Swansea.
Swansea made the better start, grabbing the lead after eight minutes when an unmarked James Thomas beat keeper Lee Harrison after latching onto Kieron Durkan’s through-ball.
Orient were back on level terms two minutes later when Chris Tate saw his first effort blocked but smashed home rebound past Neil Cutler after Gary Alexander had chested down Matthew Brazier's cross.
Orient created a host more chances as Wayne Purser, Alexander and Tate all went close but could extend their lead before the break.
Thomas missed a great opportunity to give Swansea a dream start early in the 2nd half when he fired over from close range.
And Brian Flynn’s men were left to rue that miss when Orient doubled their advantage on 52 minutes when Michael Turner, on loan from Charlton, headed home Matthew Lockwood's excellent right wing corner.
Orient made sure of the win midway through the second half as Lockwood executed another perfect delivery and Tate headed home his sixth league goal of the season.
Orient manager Paul Brush had set his side a 50 point survival target which they reached with this victory and he admitted: "I slept well last night - but will sleep even better tonight. But 50 points is only a starting point with the players we have here I know we can go on and do something better.†He added: "This was a very important win, the players worked hard and thoroughly deserved it.†Swansea boss Brian Flynn admitted: "We were second best today. We didn't do well defending crosses - and Orient could have had six.†The struggling Swans meet Exeter on Monday in a relegation six-pointer and Flynn said: "It's a massive game for us, the players don't need to be told that they were not good enough today.â€