Lincoln, on the ropes in the first half, hit back with a spectacular leveller from Richard Butcher 20 minutes from time.
The point stretched Orient's unbeaten run to seven - and it was Lincoln's fifth draw on their travels this season.
Watched by their biggest home gate of the season, 4,837, Orient started well and leading scorer Alexander had two headers saved by Lincoln goalkeeper Alan Marriott in the first 14 minutes.
So it came as no surprise when the home side took the lead a few minutes later.
A clever corner routine allowed Matthew Lockwood the time and space to latch on to the ball and when his 20-yard drive was parried by Marriott, Alexander popped up to head home the rebound - his 9th of the season.
Orient almost increased their advantage on the half hour when Alexander set Lockwood galloping free down the left and his 25-yard drive thudded against Marriott's left hand post.
Orient almost paid the price for not making the most of their chances when a mistake by Justin Miller just before half time let in Nat Brown who lobbed the ball over keeper Garner - but Miller atoned by racing back and scrambling it off the line.
But the complexion of the game changed in the second half and although Jabo Ibehre and Alexander went close to stretching Orient's advantage it was City who started to take a vice like grip.
Home keeper Garner did well to stop an effort from lively substitute Derek Asamoah but there was no denying the visitors and when the Orient keeper could only half clear a corner Butcher fired home a super strike from a tight angle.
After that City almost won it as Asamoah shot wide and then skipper Dean Keates saw a close-range effort spectacularly tipped over the bar by Garner.