The lanky 31-year-old from Johannesburg saved all three break points he faced in the second set with aces in advancing to Sunday's championship match against the winner of a later showdown between Germany's eighth-ranked Alexander Zverev and Japan's ninth-ranked Kei Nishikori.
Anderson seeks his fourth and biggest career ATP title on the Washington hardcourts after Winston-Salem in 2015, Delray Beach in 2012 and Johannesburg in 2011.
"It would mean a lot," Anderson said. "I'm really excited to be there. I think I can take a lot from this week. It's a great start to the summer. It will be a terrific opportunity."
The 58th-ranked left-hander seeks her first title since 2014 at Pattaya City. Makarova's only other WTA crown came at Eastbourne in 2010.
Sock, a champion this year at Auckland and Delray Beach, had not dropped a set all week and had been broken only once, but Anderson changed that in short order.
Anderson broke Sock at love for a 2-0 lead and held serve from there to take the first set, saving a break point in the last game with a service winner.
"Some of my best serves were on break points," Anderson said. "I'd like to have brought out some of them earlier but I'll take them.
"I play my best tennis when my back is against the wall. I'm trying to channel that into my tennis."
Anderson, who ousted top seed Dominic Thiem in the third round, had not reached a final since his 2015 Winston-Salem title.
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Sock ripped the stadium court he played upon all week, saying, "I don't think I'll be back at this tournament, probably, in the future. Probably the worst court of the year. Speed, bounces, everything. Pretty shocking. Probably the worst court on the tour."
The world number 19 was also unhappy about an incorrect line call that forced a replayed point on a break chance.
"It's pretty frustrating," Sock said.
Anderson, whose 62 aces this week lead the field, is 0-2 against Zverev and 1-4 against Nishikori. He fell to Zverev in the second round at Washington in 2015 and lost to Nishikori in 2010 qualifying.
Zverev, a 20-year-old who reached a career ranking high this week, seeks his fourth title of the year after crowns at Rome, Munich and Montpellier.
Nishikori is playing his first event since a third-round exit at Wimbledon. Zverev reached the fourth round there, his deepest run yet in a Grand Slam tournament.
Nishikori seeks his 12th career ATP title while Zverev chases his fifth.
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