Golding claimed 10 of the last 11 games to secure a 6-4, 6-1 victory over Gojowczyk, who defeated top-10 player Milos Raonic last week on his way to the quarter-finals of the Gerry Weber Open in Halle. That ended a five-match losing streak for the 20-year-old, who needs two more wins to earn a place in the main draw at Wimbledon for a second time. He was given a wild card in 2012 and next meets the Swiss Marco Chiudinelli.
The only other British winner was Brydan Klein, who was leading Maxime Authom 6-3, 1-0 when the Belgian retired. Six other British men lost their opening matches, with David Rice and Josh Milton the only two to win sets.
There was victory for Aljaz Bedene, the Slovene who is hoping to switch nationality to British, though, while Steve Darcis also reached round two. The Belgian caused one of the biggest shocks of last year's tournament by defeating Rafael Nadal in the opening round but sustained a shoulder injury which required surgery.
He has only just returned to action and needed a wild card to get into qualifying. "Last year was maybe the best moment of my career and at the same time maybe the worst one," he said. "I have to enjoy this because it's been so tough."
The British duo Dan Evans and Kyle Edmund, both of whom have been given wild cards into the main draw at Wimbledon, lost in the first round of the Aegon International at Eastbourne, meanwhile, as did Agnieszka Radwanska, the women's top seed.
Evans, the British No.2, lost 6-2, 6-3 to the German Tobias Kamke, while Edmund went down 7-6 (7-5), 6-3 to the American Sam Querrey. Fifth-seed Ivo Karlovic was another first-round casualty against France's Jeremy Chardy, while the eighth seed, Federico Delbonis, lost to Martin Klizan.
Radwanska suffered her third successive first-round loss at the competition against Anastasia Pavlyuchenkova of Russia.