It was only Orient's fourth win of the season but Alexander's sixth goal of the campaign made it a miserable afternoon for Huddersfield, who had defender Martin McIntosh sent off and five other players booked.
Orient dominated the first half for long periods as they knocked the ball about with their midfield four taking a vice-like grip. But for all their possession clear-cut chances were few and far between.
O's winger Wayne Corden tried his luck from distance and saw an effort skim the bar, while at the other end Town defender David Mirfin fired over from close range following a corner.
It came as no surprise when Orient took the lead on 28 minutes following a flowing move that included Craig Easton, Justin Miller, Alexander and it was Corden's cross from the left that the Orient striker headed home from six yards.
Orient should have stretched their advantage on 41 minutes when Corden's excellent cross from the right was headed inches wide by midfielder Easton.
However, it was Town who were guilty of the miss of the match when O's old boy Gary Taylor-Fletcher crossed from the right and Mark Hudson smashed the ball against the bar from three yards.
It was a costly miss as the ever dangerous James Walker went within whisker of adding a second for the home side moments later.
Town boss Peter Jackson threw substitute Luke Beckett into the action at half-time but he could not lift the visitors even though they started the second half with a flourish.
Taylor-Fletcher went close with a snap-shot but Huddersfield's revival hopes were shattered on the hour when McIntosh sent Alexander flying and picked up his second yellow card from referee Darren Deadman.
Town did go close to levelling but Alton Thelwell was the Orient hero when he hacked Andy Booth's header off the line.
But Orient should have won the game more comfortably and Walker twice went close to stretching their advantage.