After enjoying the better of the first half, the weary-looking hosts were forced to defend for long spells after the break as the Bairns grew into the contest.
Alfred Johansson made three changes from the side which drew 1-1 with the Finnish side in the first leg of their European qualifier on Thursday.
Nineteen-year-old Mikey Booth made his first Scottish Premiership appearance, while Jamie Knight-Lebel and Ibrahim Said also came into the starting XI.
Following a difficult start to the season, which has seen them exit the Premier Sports Cup at the group stage before losing their league opener to St Mirren, John McGlynn made six changes to his Falkirk side, including a debut for new signing Finley Barbrook.
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The Bairns boss was then forced into a further change when Joe Gardner suffered an injury in the warm-up and was replaced by Ethan Ross.
Home striker Tawanda Maswanhise dragged his effort wide as the Steelmen registered the first chance of note in the 12th minute.
Falkirk immediately threatened at the other end, with Ross drawing a save from Alex Paulsen.
Maswanhise almost broke the deadlock in the 27th minute when he stabbed an effort just wide from Emmanuel Longelo's cross.
The Zimbabwean appealed for a penalty in the aftermath, claiming his shirt had been pulled by Liam Henderson but referee Chris Graham instead awarded a corner.
The visitors had the crossbar to thank a minute later as Said's thunderous effort smashed against the woodwork, while Maswanhise's snap-shot flew off target just before half-time.
Both teams made changes at the interval, with Booth replaced by Alex Lowry and the Bairns introducing Craig Sibbald for Finn Yeats.
Paulsen comfortably gathered Aodhan Doherty's free-kick as Falkirk made a positive start to the second half.
On the hour mark, Maswanhise perhaps should have done better when he met Longelo's delivery, sending his effort over the crossbar.
Johansson was forced into another change in the 64th minute when skipper Tom Sparrow limped off. Jake Girdwood-Reich came on in his place, while Johnny Koutroumbis was introduced for Martin Moormann.
As the game approached the final 20 minutes, the hosts were looking increasingly tired.
Girdwood-Reich did well to turn Paul McGovern's dangerous cross behind for a corner before the resulting set-piece was cleared to safety.
Motherwell almost grabbed the opener on the counter-attack moments later. Lowry's threaded pass landed perfectly at the feet of Koutroumbis, but he got his shot all wrong and fired wildly off target.
The game began to open up as both teams chased the three points and Falkirk loanee Ben Krauhaus was not far away with a curling effort which drifted inches past the post.
Barbrook was next to go close for the Bairns, lashing a goal-bound drive which crept wide after deflecting off Girdwood-Reich.
Neither side could find the breakthrough, with Motherwell forced to settle for a point before turning their attention back to Europe.
