Tony Philliskirk's side returned to the Leyland County Ground with a 0-0 draw against Middlesbrough in the U18 Northern Premier League.
Both sides took a little while to get going on a wet and breezy afternoon in Lancashire.
As the Clarets' first real opportunity came with 20 minutes played, as the in-form Unwin, who grabbed two goals midweek in the Clarets Cup semi-final, saw his low drive saved by Max Metcalfe.
Shortly after, Boro had a chance of their own, as Alfie Doherty's free-kick was tipper over the bar by Lewis Thomas in the Burnley goal.
But just before the break, winger Kade Ratchford had a chance to give the hosts the lead, but his effort from inside the area was again denied by the towering Metcalfe, between the Boro sticks.
The Clarets started the second-half on the front foot, as Corey Brennan, who was playing as a striker rather than his usual central midfield role, connected with an overhead-kick which sailed just over the bar.
Moments later, Philliskirk's side came close again as Unwin's attempted lob over Metcalfe from 25-yards, bounced back off the post.
And the home side, who were dominating the attacking third, came close once again, as the lively Unwin fired just over the bar from just outside the area.
But Boro then had a great opportunity of their own, as Callum Kavanagh broke through on goal, only for Thomas to make a great save.
But despite late attacks from both sides, both defences stood strong on an afternoon with challenging conditions, to keep their opponents at bay.
Philliskirk's side are next in action next weekend, as the Clarets travel to Liverpool.
BURNLEY: Thomas, Connolly, Rooney, Gallagher-Allison, Dodgson, Armstrong, Moonan, Coppack, Ratchford, Unwin, Brennan (Hugill 82).
Not used: Waller, Carson, Behan, Smyth-Ferguson.
Clarets travel to Merseyside for U18 Premier League clash