Luke Rodgers fired the Magpies in front with a clinical finish in the 26th minute after a long ball over the top by right-back Brendan Moloney. It was the 27-year-old's fourth goal of the week following his midweek hat-trick at Lincoln City.
The Robins equalised through Hammond in the 75th minute, the striker spinning sharply to fire in from close range after substitute Julian Alsop had flicked on Lee Ridley's long throw.
Cheltenham, who had a Justin Richards strike on eight minutes ruled out for offside, carved out a number of openings with Michael Townsend's volley grazing the bar on 43 minutes. Barry Hayles also rattled a post with a volley just after the interval.
In the first half David Bird had ghosted in at the back post but headed straight at Kasper Schmeichel from six yards.
The young County keeper's big boot was the most potent weapon for the visitors with Lee Hughes nearly poking a huge clearance past Robins keeper Scott Brown on 10 minutes.