Former Robins loan striker Sam Smith opened the scoring, slotting past Scott Flinders after Shilow Tracey's ball was misjudged by Lewis Freestone in windy conditions.
The U's doubled their lead in the 52nd minute when George Williams' ball from the right was smashed into his own net by defender Mattie Pollock.
Ironside was set up for Cambridge's third in the 63rd minute, headed in his second from Adam May's free-kick in the 73rd minute and then lashed in his third from substitute James Brophy's flick two minutes from the end.
Story of the match
The first chance of the game fell to Cheltenham as Liam Sercombe shot from the edge of the box, but Dimitar Mitov was able to make the save.
Cambridge then had a double opportunity when Freestone blocked a shot by May and Flinders stopped Smith's close-range effort.
On 25 minutes, a well-taken free-kick by Daniel Crowley that struck the side netting represented the Robins' best chance.
Flinders was left scrambling when Weir and May had shots that narrowly missed, but the U's would soon make all of that pressure pay off.
The hosts opened the scoring in the 37th minute when a lofted ball over the top by Tracey was run on to by Smith, who finished into the bottom corner.
Seven minutes into the second half, Cambridge doubled their lead as another lofted ball, this one by May, Williams played it across the six-yard box that Pollock accidentally turned home.
Alfie May hit the crossbar just after the hour mark, marking Cheltenham's best opportunity of the second 45 minutes.
Smith played in Ironside and his left-footed strike beat Flinders at his near post to make it 3-0. It was four when May's free-kick was met by Ironside's head, but it was his last goal that was the most stylish.
Jack Lankester's zipped pass found the feet of Brophy, whose back-heel across goal put it on a plate for Ironside to complete his hat-trick and a memorable night for the U's.
Man of the match: Adam May
Ironside may have recorded a hat-trick, but it was the Cambridge midfielder who set up several chances, pressured the Cheltenham defence with a couple of shots of his own and dictated the pace of the U's attack.