Danny Wright's second half header gave Cheltenham their sixth victory in seven games away at fellow high fliers Woking. During a match with few real chances, Wright's powerful header from a Munns' 67th minute corner was the difference and moved the Robins up to second in the National League.
In an opening 10 minutes where Cheltenham had more of the ball, it was the hosts who managed to create the better chances. Robins' old-boy Craig Braham-Barrett did well down the left before firing in a dangerous low cross, only for Harry Pell to get back well and intercept.
John Goddard then tested Dillion Phillips in the Cheltenham net with a stinging low shot which was held well.
Kyle Storer had a shot from the edge of the box which sliced just wide before Danny Wright almost capitalised on some awkward defending, nipping in to poke a shot past the stranded keeper, only for the ball to miss the target.
Both teams struggled to create many clear cut chances with both sides defending well. Cheltenham should however have taken the lead on 26 minutes when a good cross in from Kyle Storer found Rob Dickie unmarked at the back post. However the defender couldn't keep his header down from six yards and the ball flew over the bar.
The visiting fans thought they had scored in the 31st minute when Jack Barthram played in Danny Wright inside the box, only for the striker's shot to hit the side netting.
Cheltenham continued to create the clearer chances and Danny Wright will feel he should of scored when Amari Morgan-Smith floated in a perfect cross for him at the back post, his powerful header was too close to Woking keeper Jake Cole who pushed the ball over the bar.
With neither team able to hold onto the ball in the final third, the first half ended 0-0 with no side really on top.
Woking started the faster of the two teams, Jack Barthram getting back just in time to head to safety after Bruno Andrade had done well down the Woking right. Cheltenham were not alive to the resulting short corner and a header from close range deflected off Barthram and just went over the bar.
Cheltenham finally got a hold of the second half and were denied taking the lead by a great double-save from Cole in the Woking net, first saving a Morgan-Smith shot before flinging himself full length to deny Pell's rebound effort.
With the game lacking a piece of quality inside the final third to break the deadlock, Jake Caprice thought he had produced it when he got to the byline and fizzed in a great ball across the goal, only for it to somehow miss absolutely everyone and out to safety.
Woking were made to pay for this in the 67th minute when Cheltenham striker Danny Wright rose highest at the back post to head home a Jack Munns' corner, his fifth goal of the campaign.
It was looking likely that a set-piece would provide the first goal with neither side able to easily break down the others' organised defense, and so it was today.
Even after the goal, there were not many chances created, even after both managers had made substitutions. Billy Waters and Asa Hall coming on to replace Jack Munns and Danny Wright respectively for the Robins.
As the match headed into the final few minutes, it was Cheltenham who looked the stronger, keeping possession and preventing Woking from creating any meaningful attacks. Billy Waters thought he had doubled the lead, but Cole again produced a top drawer save to keep it at 1-0.
Woking threw men forward at the death to try and snatch an equaliser but were unable to really trouble Dillon Phillips and the match ended 1-0 to Cheltenham, much to the delight of the 195 travelling fans.
Jake Caprice (Giuseppe Sole, 81), Brian Saah, Terell Thomas, Craig Braham-Barrett
Bruno Andrade, Keiran Murtagh, Jimmy Keohane, John Goddard (Kadell Daniel, 81)
Harry Cardwell (Joey Jones, 56), Daniel Holman
Jack Barthram, Rob Dickie, Aaron Downes, Daniel Parslow, George McLennan
Harry Pell, Kyle Storer, Jack Munns (Asa Hall, 73),
Danny Wright (Billy Waters, 82), Amari Morgan-Smith
Attendance: 2035 (195 away)