Visiting manager Paul Hartley was pleased to see his team bounce back from their midweek defeat by Inverness Caledonian Thistle and said: “It was a terrific result for us, especially after midweek. The team is starting to gel and you can see signs of good things.
“We kept a clean sheet and credit to the players.”
Andrew Nelson, on loan from Sunderland, had a golden opportunity to fire Falkirk into the lead after five minutes but he shot wide from only 12 yards out.
However, the visitors went ahead with what proved to be the winner as Sibbald, pictured, grabbed his first goal of the season after 20 minutes.
There seemed to be little danger when Derek Gaston came to claim a Louis Longridge corner but the goalkeeper flapped at the ball and it fell to Sibbald who had a simple task to slot into an empty net.
Only the bar prevented Falkirk doubling their advantage before the break when Longridge’s effort deflected off Thomas O’Ware and over Gaston before bouncing off the woodwork.
Morton struggled to break down a resilient Falkirk defence and were thwarted by three separate goal-line clearances to suggest it wasn’t going to be their day.
Robert Thomson had two goal-bound efforts cleared off the line by the impressive Tom Taiwo and Lewis Kidd before goalscorer Sibbald proved his worth at the other end clearing off the line during the closing stages.
Falkirk’s margin of victory would have been more comfortable had Longridge and Sibbald converted good chances.
Jim Duffy, the Morton manager, said: “I think we were worthy of a point. We made a mistake for the goal but we had at least three efforts cleared off the line.”