A late own goal from Oliver Ryan denied Lincoln their first win since August.
The Imps, who sacked manager John Schofield in midweek, made five changes and produced their best performance of the season, dominating the first half.
Ben Wright swept them ahead on the stroke of half-time after a header from Adie Moses came back off the bar.
Mark Tyler kept out Louis Dodds, who then hit the bar with the rebound, before substitute Rene Howe's cross was turned into his own net by Ryan.