Mitchell Rose put the visitors ahead after the break, but Liam Kelly levelled before the late drama in east London.
Orient made the first chance as Sandro Semedo’s cross fell perfectly for Ollie Palmer, but the former Stags ace lashed over from eight yards.
It was a missed opportunity for the Brisbane Road outfit and the visitors should have made them pay in the 22nd minute.
O’s defender Yvan Erichot bundled Krystian Pearce to the floor inside the box and referee Kevin Johnson pointed to the spot.
After a stuttering run-up and lengthy wait, Green fired the penalty over the crossbar and it remained goalless.
Kevan Hurst called Alex Cisak into action less than 60 seconds later, but the Australian was able to parry over the crossbar.
Orient briefly rallied with Semedo shooting wide from 25-yards before Mansfield’s Kyle Howkins volleyed over from close range just before half time.
Both teams began the second period slowly, although the Stags forced Cisak into another save in the 59th minute when Pearce won a header at the back post.
They missed that chance but nine minutes later they did take the lead after some poor defending by the hosts.
Hurst swung the ball in and it didn’t come for Green, but it fell for Rose at the back post and he smashed into the net.
Stags lead only lasted five minutes, though, as Orient equalised in emphatic fashion through Kelly.
Nigel Atangana found substitute Jordan Bowery, he held the ball up and passed to Kelly on the edge and he slotted into the corner.
It seemed like it would finish level in east London, but Mansfield had the last laugh as Green fired through Cisak’s legs to take the points.
Leyton Orient (4-2-3-1): Cisak 7, Hunt 6, Erichot 5, Parkes 7, Semedo 5, Kelly 7, Atangana 7, Cornick 6 (Bowery 62 7), Cox 7, Massey 7, Palmer 5 (McCallum 62 6). Subs not used: Sargeant, Kennedy, Weir, Pollock, Koroma.
Mansfield Town (4-1-3-2): Jensen 5, Bennett 6, Howkins 6, Pearce 8, Benning 7, Collins 6, Rose 7, Chapman 6 (Maguire 80 6), Hurst 7 (Baxendale 60 6), Henderson 6 (Hamilton 50 6), Green 8. Subs not used: Shearer, Taft, Hoban, Hemmings.