Brad James made it back-to-back wins and clean sheets for Gateshead after they overcame local rivals Spennymoor Town in midweek.
JJ O’Donnell scored with only three minutes gone on the clock for the Heed, who were without a fixture at the weekend.
The two wins in succession for Gateshead leaves them in ninth after nine games in National League North.
Tyrone O’Neill and Darlington picked up three points with two games in the space of a week, beating Blyth Spartans in midweek but came up short against Gloucester City on Saturday.
The Quakers fell behind through Callum Roberts’ goal, but they were only trailing for two minutes as O’Neill played his part in teeing up Adam Campbell who levelled the scores.
Stephen Thompson grabbed the winner for Darlington with 15 minutes to spare to help them register their first win in four games, but O’Neill and the Quakers were edged out on the road against Gloucester at the weekend through a Joe Hanks brace. Campbell notched Darlington’s goal.