The O's dominated the game but ended up having to endure a few anxious moments after Jo Kuffour cut the deficit midway through the second half.
But it was too little too late for the visitors who are still searching for their first away success of the season.
However, they were almost given a dream start after just two minutes when home keeper Glyn Garner had to tip an effort from Leon Constantine on to a post.
But after surviving that early scare Orient quickly imposed themselves on the game and the ever dangerous Ibehre saw the excellent Andy Marriott push his snap shot away for a corner.
The visiting goalkeeper was in sparkling form as he dived to push away Alexander's header, but it came as no real surprise when Orient broke the deadlock on 25 minutes.
Shane Tudor raced down the right and crossed for Ibehre to curl the ball into the corner of the net from 14 yards.
Marriott then made another superb save to deny Ibehre's excellent solo run from the halfway line.
After the interval Orient looked to have wrapped things up when Alexander latched on to Tudor's lob and fired home his sixth goal in five matches.
But Torquay refused to throw in the towel and, when Constantine held off a challenge from Gaby Zakauni, he fed Kuffour who tucked the ball home.
Torquay tried hard to force their way back into the match but it was Orient who still created the better chances and 20 minutes from time John Mackie saw a close range header pushed away by Marriott.
Alexander and Matthew Lockwood both later had efforts saved as the O's failed to give themselves some breathing space.