The striker reacted first to steer a right-foot shot into the net 13 minutes into the second half after Scott Higgins had saved well from Richie Foran.
It was a dismal day for Falkirk with their captain Steven Thomson being shown a straight red card in the second half for lashing out angrily at Calum Elliot off the ball.
Both teams looked bereft of ideas up front, although Falkirk's Pedro Moutinho threatened on a couple of occasions.
Motherwell had a chance shortly before half-time after Liam Craig generously gifted them the ball at the edge of his own penalty area, but McDonald curled his shot yards off target.
Falkirk were forced to change things at half-time and went to a back four with Karl Dodd and Liam Craig making way for Steven Thomson and Stephen O'Donnell, and Latapy pushed further forward in support of his strikers.
Yet Motherwell continued to carry more threat. Mark Reynolds should have done better when he lashed the ball over with the Falkirk defence loitering at a corner.
The breakthrough came after 58 minutes after Higgins had saved magnificently from Foran only for McDonald to produce a clinical finish from a tight angle.
Life became more difficult for Falkirk with Thomson's sending off for angrily lashing out at Elliot.