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Welshman Greenslade and his English team-mate Gillett beat Welsh pair Dan Salmon and Damian Doubler 7-7, 8-6.
Greenslade, from Cardiff, clinched the match with a dramatic wood - walking alongside the bowl and shouting encouragement as it went.
Asked how he felt as he played the shot, he said: "I just hoped and prayed . . . and thought 'don't be short'."
Gillett commented: "I never even watched, because anything can happen with Jason.
"I'm just really pleased for him."
Salmon and Doubler beat Jamie Chestney and Mark Davies 7-8, 9-1, 1-2 to reach the final.
Greenslade and Gillett saw off David Gourlay and Mervyn King 8-4, 3-7, 1-2 to set up their title chance.
Jason Greenslade and Les Gillett won the World Indoor bowls pairs title at Hopton-on-Sea, Norfolk.