Tom Bradshaw scored his third goal in as many matches as Walsall secured a hard-fought victory over in-form Bradford.
Bradshaw's 12th goal of the season gave the Saddlers a first-half lead, before Lee Evans's volley draw Bradford level after the break.
But Lalkovic's cool finish with 16 minutes remaining earned Walsall their first win in three matches.
The Saddlers showed two changes from the side that lost 2-1 at Swindon on Tuesday night.
Milan Lalkovic and Kieron Morris were recalled to the starting line-up, with Anthony Forde and Jordan Cook dropping to the bench.
Bradford, who were unbeaten in ten matches, threatened first, Billy Clarke crossing for the unmarked James Hanson to head straight at Neil Etheridge.
Walsall dominated possession in the early stages and opened the scoring on 11 minutes.
Lalkovic’s 25-yard drive deflected fortuitously into the path of Bradshaw, who, one-on-one with Bradford keeper Ben Williams, finished with aplomb.
It was Bradshaw’s third goal in as many matches – his 12th of the season – and the first goal Bradford had conceded in over 11 hours of football.
Walsall, who slipped to fourth after Tuesday’s cruel defeat at Swindon, were totally dominant.
The lively Rico Henry instigated one incisive counter-attack with a jinking run and a pass out to Sawyers on the left.
The Saint Kitts and Nevis international then slid the ball forward towards George Evans but the onrushing Williams gathered bravely at the midfielder’s feet.
And shortly after, Manchester City loanee Evans was inches away from finding the top corner with a bending right-footed effort from outside the box.
Phil Parkinson’s Bradford fashioned their best chance nine minutes before half-time, when Lee Evans’ low curling shot was pushed away by Neil Etheridge.
But Walsall ended the half on the front foot, with Paul Downing sending a powerful header just over the bar from James O’Connor’s whipped right-wing cross.
HALF-TIME: WALSALL 1-0 BRADFORD
Play-off hopefuls Bradford were out of sorts in the first half but made a strong start to the second period, with Tony McMahon heading Kyel Reid’s deep cross over at the far post.
The Bantams were now on top and after 59 minutes, Etheridge made a fine stop to keep out Hanson’s towering header from Stephen Darby’s accurate centre.
And moments later, Billy Knott drilled a right-footed shot just wide from distance.
Bradford’s pressure finally told on 64 minutes, when Lee Evans hit a sumptuous volley into the bottom corner from 20 yards to draw the visitors level.
But Walsall responded positively and regained their lead ten minutes later.
Saywers set Lalkovic away with a superb defence-splitting pass and the Slovakian winger coolly slotted past Williams into the far corner.
Bradford pushed for another leveller; Etheridge held Knott’s long-distance drive and Mark Marshall’s cross was volleyed over by McMahon when he really should have done better.
Sawyers fired over the bar from long range in the closing stages, and Walsall survived a late spell of Bradford pressure to hold on for three valuable points.
FULL-TIME: WALSALL 2-1 BRADFORD
Team: Etheridge, Demetriou, Downing, O’Connor, Henry, Chambers, Evans, Lalkovic (Cook 85’), Morris (Forde 77’), Sawyers, Bradshaw.
Subs not used: MacGillivray, Taylor, Baxendale, Preston, Flanagan.