Green had missed a first half spot kick for the Stags before Mitchell Rose’s second half effort put them in front.
Liam Kelly’s second goal in as many games levelled matters, but with the game seemingly ending in a draw Green made up for the penalty miss to net the winner.
Orient made one change to the starting line-up which won 2-1 at Grimsby last weekend, with goalscorer Ollie Palmer in place of Jordan Bowery who moved to the bench, while Paul McCallum also made a return to the matchday squad.
It was the hosts who started on the front foot, forcing the first corner after just three minutes and after the set piece was only half cleared to Sandro Semedo the Portuguese youngster let fly from 25 yards, only for his team-mate Tom Parkes to get in the way of the effort.
Up the other end Alex Cisak was able to hold at stretch a Matt Green header following Kevan Hurst’s floated ball in before Orient began to press once more.
A lovely interchange between Dean Cox and Harry Cornick resulted in the latter putting in a pin-point cross from the right and former Stag Ollie Palmer headed narrowly over.
It was to be the first chance for Palmer and he missed a great opportunity minutes later when a Semedo cross fell to him and he took one touch before flashing the effort well over the bar.
Cox continued to be involved, linking up well with Massey down the left and after a one-two, the former Colchester man curled an effort just wide of the target.
Despite being on the front foot in the early stages, it was the Stags who had the best opportunity to break the deadlock when Yvan Erichot brought down Krystian Pearce in the box and referee Kevin Johnson had no hesitation in pointing to the spot.
Up stepped Matt Green to take the spot kick after a short delay, however, the striker blazed the effort right into the back of the Tommy Johnston Stand and the game remained goalless.
Despite the penalty miss, Mansfield continued in the ascendancy and it took another goalline clearance from Parkes to deny the Stags the opener a minute later.
As the half drew to a close it was Orient who were on top, spreading play from side to side and it was Semedo who fired the next effort goalwards, however, it was just dragged wide and minutes later Cornick squared the ball for Cox, but unlike his header against Stevenage, this one was off target and behind for a goal kick.
Right on the stroke of the half-time whistle Kyle Howkins was only able to glance a header over the bar as the match remained goalless at the break.
No changes were made by either side at the interval, but former O Darius Henderson only lasted five minutes into the second half and was replaced by CJ Hamilton.
Just like the first half, the O’s won the first corner of the second period through the endeavour of Palmer, and Cox’s set piece found the head of Parkes but the central defender directed the header wide.
Alex Cisak was called into action just short of the hour mark as he produced a fine stop to deny Pearce’s header, before the O’s made a double change with Palmer and Cornick making way for McCallum and Bowery respectively.
Pearce then almost scored up the other end as got a head on Cox’s cross and fortunately for the defender the ball went behind for a corner.
The Cox-Parkes combination came into effect once again for a set piece, as the former’s inswinging corner found the head of Parkes once more, but disappointingly the effort was off target.
Just with Orient in the ascendancy they were dealt a hammer blow when Mansfield took the lead on 68 minutes. Hurst’s delivery from the left found its way through to Mitchell Rose at the back post and he lashed the finish past Cisak in the Orient goal.
The lead didn’t last long though as Orient were level inside five minutes. Some lovely work down the right from Orient saw Atangana feed the ball into Bowery who laid the ball back into the path of Kelly who curled the effort into the top corner past Jensen.
Time was ticking away but the hosts remained on the front foot and Kelly tried his luck from 25 yards but this time saw his effort fall wide of the near post, before no-one could get on the end of a teasing Cox cross.
However, the hosts found themselves behind with a minute left on the clock as Green pounced in the box and fired low past Cisak.
Orient pushed forward and McCallum was inches away from getting on the end of a fierce Massey cross, but with that went any chance of the O’s salvaging a late point.
Orient: Cisak, Hunt, Erichot, Parkes, Semedo, Cornick (Bowery 62), Atangana, Kelly, Massey, Cox, Palmer (McCallum 62).
Subs: Sargeant, Kennedy, Weir, Pollock, Koroma.
Goals: Kelly (73)
Booked: Palmer (30), Kelly (47)
Mansfield Town: Jensen Benning, Howkins, , Pearce, Rose, Collins, Chapman (Maguire 80), Hurst (Baxendale 80), Green, Henderson (Hamilton 50).
Subs: Shearer, Taft, Hoban, Hemmings.
Goals: Rose (68), Green (89)
Attendance: 3996 (217 Mansfield Town fans)
Referee: Kevin Johnson