The Hatters dominated the first half and led through Sam Parkin's 24th-minute header.
But a second-half fightback from the visitors saw Gillespie find the net late on to keep their survival hopes alive.
In blizzard conditions and kicking against a strong wind, Luton started positively with David Bell dragging a 20-yard shot wide three minutes in and Lewis Emanuel following suit two minutes later.
With both sides struggling to cope with the heavy pitch, the first passing move didn't materialise until the 16th minute when Ryan Charles dummied Richard Jackson's cross, opening up an opportunity for Parkin, whose scuffed ten-yard shot was cleared off the line by Shane Duff.
From the follow-up, Matt Spring rifled the ball straight at Shane Higgs.
Cheltenham had little to offer with Scott Brown's wayward 30-yard effort in the 21st minute their only attack of note.
Instead, the Hatters went ahead three minutes later when Parkin won the ball and released Paul McVeigh, whose 20-yard strike deflected wide off Duff.
From the resulting Bell corner, the unmarked Parkin was allowed to head home from six yards through the arms of Higgs.
The rest of the half was all Luton as Spring tested Higgs in the 31st minute, Charles slid Emanuel's cross wide at the near post a minute later and Emanuel then saw a 30-yarder tipped wide by Higgs in the 36th minute.
Higgs continued his busy afternoon's work by tipping over a Bell free-kick which deflected off Craig Armstrong in the 40th minute and then blocking McVeigh's 18-yard drive on the stroke of half-time.
The Robins finally mustered their first shot on target ten minutes into the second period when David Bird's curling 20-yard free-kick was superbly tipped over by Dean Brill after Spring had fouled Damian Spencer on the edge of the area.
Another Cheltenham free-kick from a similar position almost gave the visitors a leveller in the 65th minute when Spencer found himself in the clear after Alan Wright's effort was blocked, but Brill produced an excellent one-handed save.
The visitors kept up the pressure as Jeremy Gill smashed a scorching 35-yard drive just wide in the 68th minute and Ashley Vincent somehow headed over from a yard out after Bird's cross over Brill six minutes later.
The goal Cheltenham had been threatening duly arrived nine minutes from time when Vincent found Gillespie running into the left-hand side of the area and the winger slipped the ball under Brill from 12 yards to earn a point.