The hosts went ahead five minutes later though, as Burns nodded home Danny Hylton's cross following an incisive breakaway.
Tareiq Holmes-Dennis was a constant attacking threat from midfield and saw two efforts blocked, but Dunn was lively on the counter for Cheltenham and Ryan Clarke had to be alert to smother the ball at the feet of the Liverpool loanee in the 27th minute.
Burns came close to adding a second 10 minutes before the interval, but his fizzing strike flew inches wide of the far post.
Four minutes before the break, Dunn's lively first-half performance was rewarded with a goal as he guided Lee Vaughan's pass into the bottom corner.
Two minutes into first-half stoppage time, fellow Liverpool youngster Kevin Stewart netted for the visiting side to ensure they entered the half-time break a goal ahead.