The opening minutes of the match passed without incident at either end before Glenrothes took the lead in the 12th minute when Reece Brown was given far too much time to shoot and found the net from 25 yards.
Glens dominated proceedings for the rest of the first half and the men in red wasted several good chances.
Early substitute Ian McManus fired a shot over the bar following good work down the left by Cammy Lumsden, Blair Smart headed the ball straight at Kyle Moran from an unmarked position at the back post and a great cross by Callum Kinnes went out for a goal kick.
Brown also sent a free header over the bar on the half-hour mark yet Glens eventually added a second goal in the 43rd minute.
Blair Smart hit the bar with a header from a corner kick but former St Andrews United right back Dylan Honeyman reacted quickest to the rebound to net from close-range.
Kyle Sneddon then collected the first yellow card of the afternoon for scything down Kinnes, though the resulting free kick was easily cleared by Jack Rollo.
Glenrothes thus led 2-0 at the interval and Brown missed another glorious chance to add to his tally at the start of the second half by blazing the ball over Moran’s crossbar.
Grady subsequently missed a good opportunity at the other end by dragging a shot wide of Crowe’s right-hand post but Glens moved further ahead in the 59th minute when McManus found the net following a goal-mouth scramble.
Not surprisingly, Glens continued to press forward in search of further goals towards the end of the encounter, though a combination of poor finishing plus brave defending kept the score fairly respectable.
They did hit the post on two occasions during the final half an hour yet the home players were guilty of sending too many shots wide of the target.
United eventually managed to grab a consolation goal three minutes into injury time through substitute Harris Haleef, who chipped the ball over Crowe to score his first ever goal in the East of Scotland League.