Stonebridge was on target for City as they progressed in the FA Trophy
Truro City twice came from behind to beat Cinderford Town 4-2 to win their first ever match in the FA Trophy.
Cinderford, who like City are unbeaten in the Southern League's Division One South and West, took the lead just before the half-hour mark.
Matt Hockley equalised on 40 minutes, but after conceding a second goal Andy Watkins got City back on level terms.
Ex-Plymouth Argyle man Ian Stonebridge then gave City the lead before Watkins sealed the win with a late penalty.
City's director of football, Chris Webb, told BBC Radio Cornwall it was critical City did not do a repeat of their midweek FA Cup exit at Chippenham Town.
"It was a big boost for us really because you don't want to go out of two cup games in a matter of a week," he said.
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