The first-half was scoreless, but Reza Davies had a hand in the first two second-half goals, which set Warren on the way to victory.
He converted a penalty given for hand ball before setting up Tierney for the second goal.
When an Andy Ginnshot came back off the post Tierney, a former Ballymacash player, was on hand to tap in.
Stevie McDonagh made it 4-0 with the best goal of the match before Dale Gilmore pulled one back late on, though Ballymacash had several strong shouts for penalty awards.
All The Other Matches
Jim McMullan put Glaston ahead in the big match of the day, but Ballymacash YM came back to level 1-1.
Sandy Row took advantage with a 3-2 win over South Antrim, which stretches their lead at the top and they have games in hand.
Their scorers were Joe Trainor, Stephen Baxter and Dylan Rodgers.
1st Lisburn beat Belvoir FC 2-0.
Cregagh Wanderers surprisingly crashed 5-1 to Ballymacash Rangers III, but other results went their way though Woodvale YM beat 1st Lisburn II 3-1.
Colin Valley III and Warren YM II drew 1-1 and Orangefield OB III had a 3-2 win over Bloomfield III.
Taughmonagh YM II beat Belvoir FC II 7-1.
Victoria Athletic are back on their own at the top of Division 2 following a 3-0 win over 10th Old Boys thanks to goals from Joe McCall, Nick Craig and Paul Cairns.
Ballymacash YM III had no match and Moira Albion II were held to a 4-4 draw by Sandy Row II.
South Antrim II beat Harmony Hill 3-2 and Newtown Forest III had a 5-3 win over Lambeg Rangers II, whose scorers were Jack Payne 2 and Anto Flavin, a penalty.
Gordon Hanna Trophy
Taughmonagh YM had a 5-0 win over FC Utd Lisburn with goals from Curtis Moorhead 2, Barry Bloomer, Gary Nelson and Stephen Hislop.
Michael McKee 4 and Graham Kennedy 3 led the way when Lambeg Rangers beat Glenavy III 11-0 in a first round tie.
Other scorers were Marty Shields, Ryan Fryers, Kyle McCandless and Ryan Nixon.
All The Results
1st Lisburn 2 Belvoir FC 0
South Antrim 2 Sandy Row 3
Glaston 1 Ballymacash YM 1
Woodvale YM 3 1st Lisburn II 1
Taughmonagh YM II 7 Belvoir FC II 1
Bloomfield III 2 Orangefield OB III 3
Ballymacash Rgs III 5 Cregagh Wand 1
Colin Valley III 1 Warren YM II 1
10th Old Boys 0 Victoria Ath 3
South Antrim II 3 Harmony Hill 2
Newtown Forest III 5 Lambeg Rgs II 3
Sandy Row II 4 Moira Albion II 4
Gordon Hanna Trophy, first round
Glenavy III 0 Lambeg Rgs 11
FC Utd Lisburn 0 Taughmonagh YM 5
Warren YM 4 Ballymacash YM II 1
Tomorrow’s fixture list
South Antrim League fixtures for tomorrow (Saturday), 2pm kick-off.
PREMIER DIVISION: Taughmonagh YM v Lambeg Rgs, Belvoir FC v South Antrim, Ballymacash YM v FC Utd Lisburn, Sandy Row v Glaston, 1st Lisburn v Warren YM.
DIVISION 1: Ballymacash YM II v Belvoir FC II, Colin Valley III v Ballymacash Rgs III, Bloomfield III v Warren YM II, Cregagh Wand v 1st Lisburn II, Taughmonagh YM II v Orangefield OB III.
DIVISION 2: Glenavy III v Lambeg Rgs II, Ballymacash YM III v 10th Old Boys, Newtown Forest III v South Antrim II, Moira Albion II v Harmony Hill.
GORDON HANNA TROPHY, second round: Sandy Row II v Victoria Ath.