Gillingham were left to rue their missed chances as Orient clinch a second-half point at a foggy krbs Priestfield.
After Saturday's late win over Bristol Rovers, Mark Stimson opted for a three pronged attack with Jackson restored to the line-up
The Gills were unlucky not to take the lead just two minutes into the first half as Rene Howe raced onto Jackson's flick-on but rolled his finish narrowly wide of Jones' far post.
Five minutes later that first goal arrived, as Jackson broke clear down the right, his powerful effort was parried by Jones straight into the path of Chris Dickson who made no mistake from two yards out.
With Orient rocked by the early strike, the home side looked very comfortable and could have doubled their advantage when Danny Jackman curled a cute free-kick past Jones' near post.
36 minutes had passed before either keeper was troubled again, this time Dickson deflecting Jackson's speculative shot into the grateful arms of Orients custodian.
Four minutes before the break Rene Howe sent Jackson clean through on goal. The Gills leading scorer attempted to lob the advancing keeper but only succeeded in lofting his effort into the Rainham End.
The home side were dealt a cruel blow in the 44th minute as captain Barry Fuller was forced to leave the field after taking a blow on the hand. Chris Palmer came on to replace him in the right-back role.
Gillingham started the second half in determined mood, Adam Miller testing Jones with a low 25-yard free-kick which the O's keeper gathered at his near post.
In the 62nd minute Chris Dickson rose to meet Kevin Maher's corner but saw his goalbound effort pushed to safety by Jamie Jones on the goal-line.
Then at the opposite end Jason Demetriou found space to shoot from the left angle of the box, though Alan Julian got down sharply to save as the ball headed towards his bottom right corner.
Orient equalised in the 72nd minute after Chris Dickson was harshly judged to have fouled Jimmy Smith, from the resulting free-kick Mkandawire drilled home a low finish to level the scores.
Three minutes later the home side spurned a golden chance to retake the lead, Maher floating in a free-kick which Garry Richards could only head inches wide of Jones' right hand upright.
Ten minutes from time Chris Palmer sent a teasing ball across the face of goal but Jones was down smartly to steal the chance off the toes of the lurking Jackson, leaving the Gills with just a point to show for their efforts.
Attendance: 4753 (395 visitors)
Gillingham: Alan Julian, Barry Fuller (Chris Palmer 44), Garry Richards, Darren Dennehy, John Nutter, Kevin Maher (Andy Barcham 77), Adam Miller, Danny Jackman, Rene Howe (Dennis Oli 67), Chris Dickson,
Subs not used: Simon Royce, Josh Gowling, Curtis Weston, James Walker.
Leyton Orient: Jamie Jones, Stephen Purches, Ben Chorley, Tamika Mkandawire, Jason Demetriou, Adam Chambers (Sean Thornton 68), Charlie Daniels, Jimmy Smith, Jonathan Tehoue (Scott McGleish 68), Ryan Jarvis, Aaron Doran (James Scowcroft 84).
Subs not used: Glenn Morris, Luke Ashworth, Andrew Cave-Brown, Loick Pires.