Substitute Michael Higdon equalised for the Bairns early in the second half when he headed past Tomas Cerny.
The league's bottom side threatened early, with Michael Higdon firing powerfully over the crossbar.
However, the youngster made his third set-piece decisive after Michael Higdon was fouled by Zaliukas.
The Buddies pressed and Michael Higdon fired over following good work by Mooy and Paul McGowan.
Rangers conceded a penalty after 54 minutes but Michael Higdon's shot was pushed wide by Allan McGregor.
Bairns boss John Hughes had promised to attack, giving Michael Higdon a start ahead of midfielder Patrick Cregg.
Sam Parkin headed the Perth side in front before Michael Higdon equalised for the Buddies with a free-kick.
Falkirk went ahead through a fine turn and strike from striker Michael Higdon - his second goal in as many games.
The visitors were reduced to 10 men midway through the second half when Michael Higdon was dismissed for a second bookable offence.
Smith was full of praise for goalkeeper and captain for the day Allan McGregor, who saved a second-half penalty from Michael Higdon.
Stewart increased Falkirk's lead when he latched on to Michael Higdon's flick-on from a long ball and slammed the ball past Esson.
Substitute Michael Higdon gave his side hope after the break, meeting Luke Varney's centre with an impressive turn and left-footed shot into the net.
After an uneventful first-half, Michael Higdon opened the scoring in the 53rd-minute after Robert Olejnik tipped his shot off the underside of the bar.
Michael Higdon slipped a pass through to Lovell and the striker ran clear of the defence before toe-poking the ball past goalkeeper Janos Balogh.
The visitors applied most of the early pressure, and, from his side's second corner, Michael Higdon headed over at the back post from only six yards out.
But Alexander looked more assured moments later when he made a goal-line save to deny Steven Thomson after the midfielder had been found by Michael Higdon's cut-back.
Gus MacPherson was unhappy at referee Charlie Richmond's decision not to punish Rangers captain David Weir for an early foul on Michael Higdon in Saturday's match at Ibrox.
BBC: Rangers manager Walter Smith weary of referee criticism
Chances were few and far between in a drab first half but the game came to life when Saints striker Michael Higdon hit the crossbar after the break.
The home side's first real chance came in the 17th minute when Rangers failed to clear Kevin McBride's dangerous cross and Scott Arfield found Michael Higdon, who fired over.
First, Graham Barrett swivelled on Michael Higdon's pass but shot too close to Cerny and then he hit the side-netting after Higdon and Lovell had combined to find the Irishman space.
Langfield could have got an equaliser around the half hour mark after good work by Michael Higdon but the midfielder skied his effort over the bar from the edge of the box.
St Mirren arrived at the Granite City in buoyant mood after their emphatic 4-0 midweek win over Celtic, but Gus MacPherson tweaked his line-up, with Michael Higdon replacing fellow striker Billy Mehmet.
They had Gareth Wardlaw back from injury - while the experienced Brady returned to midfield, with Sean Lynch and Michael Higdon dropping out - but the striker was being given little supply.
The first chance came for the Lanarkshire side when Law was put through on goal by Michael Higdon, but he could only sweep a left-foot effort well wide from around eight yards.
Cerny then saved a fine dead-ball strike from Buddies centre-forward Billy Mehmet, partnering Michael Higdon up front as they sought their first three points in the SPL since a 1-0 win over Aberdeen in January.
BBC: Alex Neil (r) and Steven Thomson in action at St Mirren Park
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