Northern Ireland got their Milk Cup Elite campaign off to a winning start thanks to goals from Andrew Mitchell and Dion Charles in a 2-1 victory.
Mitchell stabbed the ball home in added time at the end of the first half, Charles found the net on 66 and Luke McCullough scored an own goal late on.
Holders Mexico drew 1-1 with the USA in Monday night's other Elite fixture.
Manchester United beat County Antrim 3-0 in the Premier section, but County Armagh defeated giants Liverpool 3-2.
County Armagh led 3-0 at half-time thanks to goals from Ciaran Corry, Caolon Flanagan and Aaron Duke and held on after the break for a memorable victory over the boys from Anfield.
"It is something the boys will remember for a long, long time to come," said Brendan Grimes, manager of the Armagh Premier side.
"It is just absolutely brilliant and full credit to the players. We had a gameplan and they stuck to it across the pitch, to the letter."
In the Elite section match at the Coleraine Showgrounds, the Danes dominated the first half but were unable to breach the home side's defences.
Northern Ireland improved significantly after the break and now play the USA in their next match at Drumahoe on Wednesday evening.
Manchester United enjoyed a comfortable start to their Premier campaign at the Ballymena Showgrounds with Oliver McBurney tapping in at the back post for their opening goal in the second minute.
Demetri Mitchell added a second with a deflected shot after 14 minutes and Ruairi Croskery made it 3-0 with a curling free-kick into the top corner before half-time.
Reigning champions Brentford got their Junior campaign off to a flying start with a 5-0 success over Ipswich Town, a score-line replicated by Watford and North Dublin SL.
Former winners Swindon lost 1-0 to five-time winners Everton and goals from Herbie Kane and Anas Abdo saw Liverpool see off County Tyrone 2-0.
Monday's Milk Cup results
Northern Ireland 2-1 Denmark
Mexico 1-1 USA
Strikers FC South Coast 6-0 TuS Altenberge
Otago Utd 3-1 Co Fermanagh
Newcastle Utd 3-2 O'Higgins FC
Cruz Azul 1-0 Cherry Orchard
Co Down 0-0 Vendee FC
SC Corinthains 3-2 Bohemian FC
Club America de Mexico 0-3 Co Tyrone
Co Londonderry 0-1 CSKA Moscow
Manchester Utd 3-0 Co Antrim
Liverpool 2-3 Co Armagh
Co Down 0-5 Watford
San Luis de Colina 0-5 North Dublin SL
Southampton 1-1 Cavan Monaghan DL
Japan FA 3-0 Co Fermanagh
Plymouth Argyle 1-2 Strikers FC South Coast
Brentford 5-0 Ipswich Town
Dundalk SL 1-2 Co Armagh
Co Londonderry 0-2 Co Antrim
Swindon Town 0-1 Everton
Co Tyrone 0-2 Liverpool