An early goal from Izzy Iriekpen and a penalty save from Swansea's French keeper Willy Gueret made it a good weekend for under pressure City boss Kenny Jackett.
The former QPR number two made two changes to the side that won at Cambridge, with Adrian Forbes coming in for Brad Maylett and Kevin Austin returning from suspension to replace Alan Tate.
The Swans went ahead in the third minute from their first corner of game.
Andy Robinson swung the ball into the danger area and when Matt Bloomer and Peter Gain made a hash of clearing the ball Iriekpen swung a boot and the ball nestled in the back of the net.
It was another half hour before Swansea threatened the visitors' goal, when Austin fed Robinson down the left and his low cross was met by Paul Connor, but his point blank shot was parried away by Lincoln keeper Alan Marriott.
This stung the Red Imps into action and Gueret, hero of the Swans' victory at Cambridge, made two fine saves from Richard Butcher and Adrian Littlejohn.
Swansea did most of the attacking at the start of the second half, but Lee Trundle was kept in check by Gareth McAuley, who was booked for an over-vigorous tackle on the striker.
Trundle did escape his maker in the 64th minute but his cross was glanced wide by Connor.
Lincoln were thrown a lifeline in the 76th minute when substitute Simon Yeo was brought down in the box by Garry Monk.
Gary Taylor-Fletcher's spot-kick went low to Gueret's right, but the keeper dived to turn the shot around the post.
This let off seemed to inspire the home side to greater effort and Trundle came more into the action, but despite going close on a couple of occasions they were unable to add to the early strike.
Back-to-back victories have given Jackett breathing space, but Lincoln were a pale shadow of the side that has contested the play-offs in the last two seasons.