Swann has been assisting caretaker boss Adie Moses at Gainsborough
Glynn Hurst's 32nd-minute goal gave Gainsborough Trinity a 1-0 victory at Solihull Moors in Blue Square North.
Hurst headed home Ashley Burbeary's cross to end a run of four defeats in Gainsborough's last game before the arrival of new manager Brian Little.
Chairman Peter Swann told BBC Radio Lincolnshire: "We set out our stall to keep a clean sheet, got the goal and then worked hard to keep the lead.
"It was good to score but even more satisfying was the way we defended."
Swann, who has been assisting caretaker boss Adie Moses, added: "It's a different kind of challenge. I've thoroughly enjoyed it and this win has made it a bit sweeter."
Little is set to take charge for the first time in Tuesday's trip to Redditch United.
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