Blues had the first half’s best chance as Max Kretzschmar was superbly denied by Scott Brown, before Steven Craig struck the post for the second successive game after the break.
The spurned opportunities looked as though they would prove costly when substitute Byron Harrison headed the hosts in front in the 68th minute.
However, Chairboys responded well and Morgan kept his cool to secure a share of the spoils after Kuffour had been brought down in the area by Cheltenham skipper Steve Elliott.
Gareth Ainsworth made three changes to his side with the available-again Josh Scowen coming in to replace the suspended Sam Togwell.
There was a complete change in attack with Matt McClure and Steven Craig in for Dean Morgan and Jo Kuffour, who dropped to the bench.
Craig thought he had broken the deadlock as early as the fourth minute when he fired low into the corner from eight yards following Marvin McCoy’s long throw, but the referee Tony Harrington had already blown for a foul on Steve Elliott.
Alert goalkeeping from Scott Brown thwarted McClure five minutes later when the striker received the ball on halfway from Matt Bloomfield and sprinted past one defender, before the keeper raced off his line to clear.
Jamie Cureton’s 10th minute header was comfortable for Matt Ingram after Elliott’s clever flick as the game began at breakneck speed.
Both sides began to settle with neither creating too much until Cheltenham right-back Mitch Brundle fired well over the bar from 25 yards in the 24th minute.
Terry Gornell then dragged a shot wide rom the edge of the area as the hosts were restricted to efforts from distance.
It was Wanderers who had the first clear opportunity of the night and it came in the 29th minute. Craig did well to hold the ball up in the corner before passing back to Arnold. The Reading loanee’s first-time cross was cushioned into Kretzschmar’s path by Bloomfield, but Brown made himself big to superbly divert away the youngster’s strike.
Chairboys were let off the hook in the 35th minute when an unmarked Ashley Vincent was unable to get anything on Sam Deering’s dangerous cross when it looked as though he was going to head the Robins in front.
Gornell’s glancing header from Matt Richards’ corner was straight at Ingram, before Blues broke and Arnold saw a strike well blocked.
Cureton headed at Ingram with time running out in the first half and that proved to be the final chance of a positive opening 45 minutes for Ainsworth’s men.
Half-time: Cheltenham 0-0 Wanderers
Blues were fast out of the traps and Craig’s powerful strike deflected behind off Elliott with the second half less than a minute old.
Arnold fired over the bar from the edge of the area, before Ainsworth made his first change in the 57th minute with Morgan replacing McClure.
Chairboys had a great chance to open the scoring in the 63rd minute as Scowen’s lofted through ball took out the defence and gave the on-rushing Craig a sight of goal, however, his shot rebounded back off the post with Brown well beaten. That was to be the Scotsman’s last involvement as he was replaced by Kuffour three minutes later.
Chairboys were made to rue that chance as Cheltenham took the lead in the 68th minute. Left-back Sido Jombati was allowed to cut in on to his right foot and his cross was glanced home by Harrison from five yards.
The home side enjoyed their spell of the game in the next five minutes, but Blues’ heads didn’t drop and they levelled in the 79th minute. The ball was played into the area and both Bloomfield and Kuffour went down in the box with a penalty awarded for Elliott’s foul on the latter.
Up stepped Morgan and he coolly sent Brown the wrong way for his eighth of the season and a deserved equaliser. The goal came at a cost though as Bloomfield was injured in the build-up and had to be replaced by Anthony Jeffrey.
McCoy tried his luck from distance four minutes time following a swift counter-attack, but his shot was always rising and cleared the bar.
Cheltenham pushed forward in search of a dramatic winner, but Matt Richards’ header, which comfortably cleared the bar, was the closest they came.
Wanderers: Ingram, McCoy, Wood, Stewart, Johnson, Scowen, Arnold, Bloomfield (c) (Jeffrey 81), Kretzschmar, McClure (Morgan 57), Craig (Kuffour 66).
Subs: Horlock, Pierre, Pittman, Jeffrey, Kuffour, Styche, Morgan.
Cheltenham: S Brown, Brundle, T Brown, Elliott (c), Jombati, Deering, Richards, McGlashan, Gornell (Harrison 52), Vincent (Noble 60), Cureton.
Subs: Roberts, Ihiekwe, Braham-Barrett, Taylor, Noble, Kotwica, Harrison
Attendance: 2,267 (242 Wycombe)