Norrie is into his fifth final of the year after previously winning at Los Cabos and has defeated the in-form Russian in a brilliant comeback.
In the opener, it only looked to be going Rublev's way going 4-1 up in quick succession against the Brit and a break to love was enough to hand him the first set 6-3.
But roles were reversed as Norrie surged into a 5-2 lead in the second set as he looked to force a decider. He finally got through it as despite missing two set points on Rublev's serve and then going 15-40 down, he held to level at 1-1.
Again he held for a 3-1 lead in the third set after previously breaking and this proved pivotal as he edged through at 6-4 in the end taking that solitary break.