Jon Daly scored a hat-trick as Dundee United eased into the third round of the Co-operative Insurance Cup at Cowdenbeath's expense.
Daly headed home from six yards from a corner and Goodwillie fired home from a similar distance after 41 minutes.
Daly drove in from 12 yards two minutes after the break and Goodwillie followed suit after 60 minutes before John Dempster fired in Cowden's reply.
Daly completed his hat-trick by firing home low from nine yards.
The Third Division Fifers were given a lesson in finishing by their Scottish Premier League opponents, who built up a two-goal interval lead before stepping up a gear in the second half.
Daly had threatened twice in the early stages before Cowdenbeath hit back with a 22-yard Jay Shields shot and a Paul McQuade effort that carried narrowly over.
But United were soon back on the attack and they notched their opening goal in the 30th minute, when Daly nipped in front of David Hay to head home a Craig Conway corner from close range.
Then, five minutes from the interval, United struck with their second goal.
This time their marksman was David Goodwillie, who pounced to shoot home from eight yards following a Conway cross.
United virtually wrapped up the match as a contest with their third goal in the 49th minute.
Goodwillie burst down the right and cut the ball back for Daly to fire a first-time right-foot shot past Hay from 14 yards.
It was Goodwillie's turn for a second goal of the night in the 61st minute.
He picked up a loose clearance 30 yards from goal and marched forward before unleashing a 22-yard drive that beat Hay at the far post.
Cowdenbeath grabbed a consolation goal in the 74th minute through substitute John Dempster, who shot home from eight yards from a McQuade cross.
But United restored their four-goal advantage in the 81st minute, with Daly again the marksman.
He fired low into the net from nine yards to complete his hat-trick and the rout.
Dundee United manager Craig Levein:
"We are delighted to be in the draw for the next round, and we hope to mount another good cup run.
"We knew Cowdenbeath would battle for every ball, and that they did throughout the game, but we were up for it, and we controlled the vast majority of possession.
"Our two first-half goals settled the tie, and then we played some great stuff in the second half.
"It was great to see Jon Daly get a hat-trick, but the finishing of both strikers was first-class."
Cowdenbeath manager Danny Lennon:
"We did well in the early part of the game, and posed them a problem or two at times, but the longer it went on, the more difficult it got for us, and in the end we were well beaten, although some of Dundee United's finishing was lethal.
"We now want to put that into action in our forthcoming fixtures."
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