Walsall took the lead in the 15th minute when Paul Downing sent a throughball over the Carlisle defence for Sawyers to collect and drill low past goalkeeper Ben Amos for his fifth goal of the season.
The Cumbrians should have been level after 25 minutes when Andy Taylor's hand struck the ball as he slid into a tackle.
But Saddlers 'keeper Richard O'Donnell blocked Lee Miller's penalty, and when the ball rebounded to the striker with the goal gaping, Miller thumped it over the crossbar from about three yards.
The Saddlers made sure of the points in the 66th minute when Lalkovic, on loan from Chelsea, took a long pass from Sam Mantom, turned inside and struck a superb right-footed shot in off the far post - his fifth goal for the club.
Carlisle defender Courtney Meppen-Walter then received a straight red card in the 87th minute for pulling back Troy Hewitt when clean through.