Orient took the lead after 14 minutes when midfielder Matt Spring blasted a right-foot volley into the net from 18 yards after the visitors only partially cleared a long throw by George Porter.
But their delight was short-lived as, four minutes later, a corner by Danny Ward caused problems for the home defence and the ball fell to Rhodes whose cheeky back-heel was helped over the line by Smith.
A Peter Clarke effort was then cleared off the line by Spring but a minute into added time in the first half, Huddersfield did go in front when a long throw by Sean Morrison was met by Rhodes, who stabbed the ball home at the near post to record his 36th goal of the season.
Orient threatened with Spring and David Mooney coming close but Rhodes put the issue beyond doubt with a minute remaining when he neatly controlled a long kick from keeper Alex Smithies before toe-poking the ball into the bottom corner of the net.
The victory moved the Terriers to within five points of an automatic promotion place while Orient remain five points above the drop zone.