Motherwell had the better of the first half, but Falkirk had a handful of chances to win it late on only to be kept out by goalkeeper Graeme Smith.
Well had the wind at their backs in the first half and immediately laid siege to the home goal. Steve Hammell's 20-yard free-kick was just a yard too high inside the opening minute with Robert Olejnik rooted to his line.
Hammell's wind-assisted corners piled the pressure on Olejnik but the goalkeeper was up to the task. He made a great-one-handed save to push a David Clarkson header on to a post and wide after seven minutes.
Two minutes later, Kenny Milne was booked for a lunge on Ross McCormack as Falkirk indulged in some desperate defending.
McCormack worked himself a shooting chance from a short corner but sliced it wildly and the Bairns survived again.
The winger burst clear again but could not pick out Stephen Hughes in the centre and Scott Arfield managed to slide in to divert the ball for a corner.
Falkirk tried to get back into things and Graham Barrett saw a shot blocked from a Carl Finnegan cross which provided some encouragement for the home support.
Olejnik slipped up when he left his penalty box and was beaten to the ball by McCormack, but again Arfield was back to prevent the winger's cross finding Hughes.
Motherwell always looked the more likely and McCormack should have scored on the stroke of half-time, but lashed the ball over from six yards.
Falkirk were better after half-time and Smith had to get down smartly top divert a Pedro Moutinho shot for a corner.
Moutinho tried his luck again moments later after beating two players but he sent his shot straight at the goalkeeper.
But chances were few and far between in the second half as the swirling wind made conditions difficult for both teams.
Moutinho did force another fine save from Smith with a close-range shot from a tight angle as Motherwell held firm.
The goalkeeper then stuck out a knee to keep out Finnegan as Falkirk threatened late on and then thwarted the Bairns striker as his net-bound header almost broke the deadlock.