Millwall dominated the first half and nearly took the lead early on. Neil Harris' disguised through ball was collected by Danny Schofield but the midfielder could only fire wide.
Lions stalwart Harris spurned a glorious opportunity to open the scoring after half an hour, sliding the ball wide with the goal at his mercy.
It was much the same after the interval but in the 69th minute up stepped Robinson to smash home from close range after some poor defending.
Eleven minutes later it got better for the Lions as left-back Scott Barron was bundled over in the area after good work from former Orient player Gary Alexander.
Top scorer Morison made no mistake from the penalty spot, smashing home his 20th goal of the season before Ben Chorley scored a consolation for the visitors in injury time, bundling home from a few yards, but it was too little too late and Orient are now closer to the dreaded relegation spots.