They will play Dutchman Jean-Julien Roger and Romanian Horia Tecau in Saturday's final.
Murray, whose brother Andy is playing Roger Federer in the Men's Singles semi-finals tomorrow, admitted after the match that Erlich's injury boosted their chances.
He said: "We got off to a slow start, especially me. We were helped out by Erlich struggling but we had to put it out of our minds.
"This is our third year together, quite a long time in doubles. We are getting our rewards and we are excited to be here.
"It will be a great match for Andy tomorrow, they have played so many times and I am sure tomorrow will be no different."