The visitors started the game brightly having a couple of opportunities to open the scoring in the opening 30 minutes.
But Town grew into the game, and they were gifted the lead on the stroke of half-time when Jamie Robson handled the ball in the box.
It gave Luke Leahy the chance to score his fourth penalty of the season - which he squeezed into the corner.
The goal gave Town a boost, and they netted a second on the hour mark when Jordan Shipley created another goal for Tom Bayliss, who had a tap-in at the back post.
It was a comfortable second-half showing for Town, who after they doubled their lead did not look like losing it.
The visitors did not match the intensity they found in the first half an hour and Town were able to see the game out with relative ease.
Town arrived at the Meadow on the back of a much-needed and much-deserved victory against Peterborough United in the FA Cup last weekend.
But they were back in league action this weekend this time against Lincoln, who have had a bright start to their League One campaign.
It was six without a win in the league for Steve Cotterill's men - partly due to the incredibly challenging fixture schedule over the last month and a crippling injury list.
Salop's record against The Imps has been good of late with them picking up a draw and two victories in their last three meetings.
And Cotterill unsurprisingly went with an unchanged starting XI from the clash with Posh just seven days ago.
Taylor Moore, who did very well at right wing-back, played there again in the continued absence of Julien Dacosta and Elliott Bennett.
Christian Saydee and Rob Street continued to lead the line-up front for Town in the boss' usual 3-5-2 formation.
They scored three goals in the first half last time out and they would love to start like that here at Meadow.
But the visitors were the ones who started the brighter almost taking the lead inside the first 10 minutes.
Marko Maorsi, who made a mistake for the goal last weekend against Posh, was dispossessed on the edge of his box by Ben House without a defender near him.
The keeper ran back towards his goal and denied the forward to prevent his side from falling behind.
Marosi was called into action again just after to deny Charles Vernam's long-range free-kick.
It was a save you would expect the keeper to make but one he made nonetheless.
Town had not offered too much of a threat at the other end and the visitors kept on pressing.
Jack Diamond made a good run down the left, evading the challenge of Matthew Pennington before linking with House.
It fell to Virtue, but his shot was saved by Marosi.
The first 30 minutes belonged to the Imps, but Shrews started to work their way back into the game in the last 15 minutes of the half.
Saydee saw a shot go wide before Street hit the byline and crossed - but there was nobody there in blue and amber to tap it home.
Town seemed buoyed by this, and Flanagan went close when his effort was tipped onto the bar by Carl Rushworth.
And Shrews would have been delighted to lead at the break when Robson handled the ball in the penalty area - giving Luke Leahy the chance to get another goal from the spot.
He squeezed the ball under Rushworth to register his fifth goal of the season.
It was a bright start to the second half for Town, Bayliss picked up the ball after a lovely combination between Leahy and Shipley, but his strike from outside the box was saved by the keeper.
And shortly after Salop did double their lead, and it was Bayliss who netted on this occasion.
A ball forward was collected by Saydee, who found Shipley out wide, and he delivered a delightful ball to the back post where Bayliss was there to turn the ball home.
It was an important goal for Town to give them a cushion, and they played some nice football at times.
Marosi had to be alert to stop Max Sanders' effort from outside the box which looked to be curling into the corner.
Cotterill introduced Rekeil Pyke and Ryan Bowman to give Salop fresh legs up front going into the closing stages.
Pennington was forced to make one block, but Town managed the closing stages with little alarm.
Shrewsbury: Marosi, Dunkley, Pennington, Flanagan, Shipley, Moore, Leahy, Winchester, Bayliss, Saydee (Bowman 80mins), Street (Pyke 80mins).
Subs: Burgoyne, Bowman, Pyke, Barlow, Hutching, Bloxham.
Lincoln: Rushworth, Poole, Sanders, Vernam (Hopper 67mins), O'Connor, Walsh, Robson, House, Eyoma, Virtue.
Subs: Wright, Hopper, Sorensen, Roughan, Draper, Ahui, Davenport