Josh Gordon pulled one back for Barrow moments after they had gone two goals down but he will rue a missed chance to equalise just before the hour mark as the Bantams escaped with the points.
Angol’s opener came in the eighth minute. He collected a threaded pass from Alex Gilliead and capitalised with a neat finish into the bottom corner.
Former Bluebirds striker Cook doubled the lead four minutes into the second half, with Gilliead again at the heart of the build-up. He got the better of Matt Platt as he tried to shepherd the ball out and set up Cook to hit his eighth goal of the campaign.
But Barrow struck back moments later. Tom Beadling’s deflected shot led to a corner which was taken short, and Josh Kay sent in a cross that fell perfectly for Gordon to head in at point-blank range.
Patrick Brough’s excellent ball flashed across the face of goal should have led to Gordon’s second but he misfired and Liam Ridehalgh denied Connor Brown following in.
The hosts did have the ball in the net 20 minutes from time but referee Sebastian Stockbridge disallowed it for a foul on goalkeeper Sam Hornby by Gordon and the Bantams held on despite late waves of pressure from Barrow.