A hat-trick from David Goodwillie helped Dundee United seal their place in the Scottish League Cup quarter-finals at Partick Thistle's expense.

The 24-year-old fired home to give United the lead before doubling their advantage before the break.

Substitute Ryan Dow grabbed a third for the hosts after Goodwillie's effort hit the post.

Christie Elliot netted a consolation for Thistle but Goodwillie capped off a resounding victory at the end.

In the all-Scottish Premiership clash it was the visitors who would have been bemused at the half-time score after they had dominated possession for long periods in the first half.

With the game struggling to get into top gear, former Motherwell player Ross Forbes tried his luck from distance with a drive which skipped just past United keeper Radoslaw Cierzniak's left-hand post.

However, Partick lacked an attacker with the predatory instincts demonstrated by the on-loan Blackburn Rovers striker Goodwillie as he latched onto to a slip by Conrad Balatoni.

The Jags stopper cut out a pass from Nadir Ciftci but slipped, allowing Goodwillie to knock the ball past Fox.

The visitors, to their credit, kept plugging away and striker Kris Doolan muscled his way past United defender Calum Butcher but found the angle too tight to get his shot on target.

Thistle were then dealt a hammer blow seconds from the interval.

Fox stretched low down at his right-hand post to save Ciftci's drive but found his good work to be in vain when Goodwillie knocked in from Mark Wilson's corner inside a packed six-yard box.

Thistle pressed for that elusive goal in the second half and Kallum Higginbotham forced a save from Cierzniak with a drive from the edge of the box.

However, United held firm and began to attack sporadically with some menace.

Balatoni cleared Wilson's whipped-in free-kick from just under his own crossbar before Goodwillie failed to get on the end of a dangerous cross from left-back Andrew Robertson.

With five minutes remaining Goodwillie cracked the post with a drive but substitute Dow was on hand to tap into the empty net.

Elliott scored in the final minute for Thistle but there was time for Goodwillie to grab his hat-trick in the first minute of added time after being set up by Stuart Armstrong.

Dundee United manager Jackie McNamara: "I'm delighted. I think we can play a lot better which is the pleasing thing.

"I thought Partick passed the ball well in the first half and they caused us a few problems without really testing our keeper. The pleasing thing for me was scoring four goals and carrying a real threat.

"It was a fantastic hat-trick, especially the last goal. It was great movement from the corner and for David Goodwillie to get a hat-trick is great for his confidence and hopefully that settles him down now and takes the pressure off him.

"It gives us an incredible lift and we'll be doing as well as we can, so we will wait and see in the draw tomorrow."

Partick Thistle boss Alan Archibald : "I thought we knocked the ball about well. We just missed that 'clinical-ness' in front of goal which we have said all season and silly mistakes at the back cost us.

"They got three goals out of nothing and we had to work for our goal.

"In the second half, at 2-0 down, we had a go and they picked us off. I don't think 4-1 is a very fair reflection of the game.

"We know where we are in the finance chain. I don't know what Goodwillie's wages are but I think he's maybe equal to five or six of our players. He is very, very clinical."

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