Wests playmaker Zac Greene had two chances to win it with a field goal.
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But then Thirroul were only a conversion away from victory themselves.
In the end, Illawarra rivals were left deadlocked at 18-all at Gibson Park.
Trailing 14-12, Wests were down to 12 men after winger Luke Towers was sin-binned for dissent, when Tony Pellow raced through the Thirroul defence and ran 85 metres to score.
But the Butchers hit back with five minutes left when halfback Jakeb Walsh produced a superb chip behind the Devils’ line for a diving Nathan Hore to gather and score.
From wide out, Walsh then had a chance to break the stalemate, but pushed the conversion attempt across the face.
Wests had the last shot at victory when Walsh failed to find touch from a penalty, but couldn’t find the game-breaking field goal despite forcing consecutive drop-outs.
“We had our chances, but I guess had Walsh converted they probably win it,” Wests coach Peter McLeod said.
“I would have liked to have held on when we were down to 12 men, we were just about to get Luke back on the field, but it wasn’t to be.
“It was a great game, I thought both teams played really well and it’s a tough place to come, so we’ll take the point.”
Thirroul coach Jarrod Costello was more annoyed about the try they conceded just before half-time, which handed Wests a 12-6 advantage at the break.
But Joel Johnson eliminated the deficit five minutes after the resumption when he barged over from close range.
The Butchers also had a second-half try to Hore controversially called back for a forward pass. But Costello couldn’t fault the Butchers effort.
“We had to absorb a bit of pressure there at the end, but I’m happy enough,” he said.
“We had a couple of defensive lapses and could have executed a bit better at times, but you can’t fault our effort.”
Elsewhere, Dante Lusio scored three tries and Josh Constable two as premiers Collegians had too much firepower for Helensburgh.
Scores were locked at 18-all at half-time, before the Dogs ran away with a 40-28 win.
On Friday night, Berkeley outmuscled Corrimal at Ziems Park.
Winger Inia Liufau finished with three tries, while Corrimal’s Liam Corey scored a double in a beaten cause.
ROUND ONE
Berkeley 32 d Corrimal 8, Thirroul drew with Wests 18-all, Collegians 40 d Helensburgh 28.
Ladder: Berkeley 2, Collegians 2, Dapto 2, Wests 1, Thirroul 1, Helensburgh 0, Corrimal 0.