Rovers looked like they would rescue a valuable point when substitute Brandon Hanlan levelled on 70 minutes.
But the hosts retook the lead a minute later when Robbie Gotts turned into his own net.
It leaves Rovers 19th in the table and with a relegation fight ahead.
See if you can spot a Rovers fan you know amongst these pictures from photographer Howard Roe.
Get more Rovers news here.
17. Lincoln 2 Rovers 1
Rovers were beaten for the seventh time in nine games after a 2-1 defeat at Lincoln City. Photo: Howard Roe/AHPIX LTD
18. Lincoln 2 Rovers 1
Rovers were beaten for the seventh time in nine games after a 2-1 defeat at Lincoln City. Photo: Howard Roe/AHPIX LTD
19. Lincoln 2 Rovers 1
Rovers were beaten for the seventh time in nine games after a 2-1 defeat at Lincoln City. Photo: Howard Roe/AHPIX LTD
20. Lincoln 2 Rovers 1
Rovers were beaten for the seventh time in nine games after a 2-1 defeat at Lincoln City. Photo: Howard Roe/AHPIX LTD