Swansea City eased into the second round of the FA Cup where they will face a trip to League One strugglers Stockport County following this win at Whaddon Road.
The Swans raced into a 2-0 lead although a late rally by the home side almost earned them a replay. A goal from Paul Connor deep into time added on sealed the result and put the Robins out of the FA Cup at the first round stage for the first time in five seasons.
Swansea dominated the first half-hour and took the lead with a well-struck goal from long-serving midfielder Kristian O'Leary after 19 minutes.
Right-back Alan Tate began the move, finding Connor with a pass into the penalty area. Connor laid the ball back for O'Leary, arriving 20 yards out and just to the right of goal and his right-foot shot speared past goalkeeper Shane Higgs and into the net.
Cheltenham were struggling to contain their visitors, who sit 14 places above them in the League Two table.
The Robins struggled to create anything of note until the 30-minute mark, when David Bird saw a shot blocked by a defender then Brian Wilson laced the rebound wide.
Martin Devaney almost equalised shortly before the break when his header was blocked by the legs of goalkeeper Willy Gueret, then defender Jamie Victory sent a curling shot just wide following appeals for a penalty when striker Steve Guinan went to ground in the box.
Cheltenham may have ended the first half on top they started the second even further behind as Swansea doubled their advantage with only seconds played.
Sam Ricketts made ground down the left and crossed to the far post where Lee Trundle was waiting to score with a soft header.
Cheltenham rallied after that and earned a way back into the game when Damian Spencer stabbed in at the far post when a free-kick from Devaney fell to him. The goal sparked an ugly 20-man confrontation although only Trundle was booked in the aftermath.
Town pressed hard for an equaliser in the closing stages, but were caught on the break in injury time when substitute Leon Britton released Connor and he lifted a well-taken shot over the diving goalkeeper.