The Australian striker contributed an equaliser and then, within a minute, set up what proved to be the match-winner for substitute Darrren Smith.
Falkirk threatened first when a free-kick from Russell Latapy was slapped away by Graeme Smith underneath his crossbar.
But David Clarkson wasted a great chance to put Motherwell in front when he took advantage of a mistake by Brian Allison, but hit the tamest of shots at Kasper Schmeichel with McDonald yelling for the ball in the middle.
Latapy did not seem affected by the horrible conditions and he sent Alan Gow clear with a fine 40-yard pass, but the striker was crowded out.
Carl Finnigan then misjudged a great through ball from Steven Thomson as he got in behind the Motherwell defence and Smith was out quickly to collect the ball.
Falkirk had another promising break when the industrious Patrick Cregg sent Finnigan clear on the right, but his through ball in search of Gow was too heavy.
If anything, it was Motherwell who looked more composed on the ball and found their men with more regularity.
McDonald and Clarkson had a neat interchange of passes after 25 minutes as the Falkirk defence opened up invitingly but the Aussie striker's 20-yard shot was just a foot too high.
Gow tried to respond but his left foot shot from 25 yards was never going to trouble Smith and it sailed well wide.
There was a blow for Falkirk when Kenny Milne hobbled off five minutes later to be replaced by Marc Twaddle which forced a reshuffle in their ranks with Tom Scobbie pulled back.
Scobbie played a big part in Falkirk's goal in the opening minute of the second half. He broke into the penalty box to lay the ball back to Gow.
The striker kept his cool to roll the ball into the path of Cregg, who drilled a low shot into the corner of the net.
Falkirk were rejuvenated by the goal. Latapy pulled a shot just a yard wide and then Thomson whipped a shot narrowly over the top.
Motherwell equalised after 66 minutes when Scobbie played the ball straight to McDonald who produced an assured finish.
A minute later, a great shot from McDonald hit the post and Darren Smith slid home the rebound.
Falkirk tried to respond and threw players forward in the closing minutes. Scobbie came closest deep into injury-time with a volley which just cleared the crossbar.