Dementieva will now face Lucie Safarova of the Czech Republic, who caused an upset by beating second-seeded Flavia Pennetta of Italy 4-6, 6-3, 6-4 in the other semifinal.
"I'm really happy to get through after such a difficult match," Dementieva said. "She is a real fighter and it's probably the most difficult win of the year for me."
Dementieva, who lost to France's Amelie Mauresmo in last year's final and who was beaten by Oudin in the second round at the 2009 U.S. Open, led 3-1 in the opening set before losing four consecutive games.
The world No. 7 from Russia broke back in the ninth game but lost her next service game.
After trading breaks, Dementieva went 4-3 up in the second set when Oudin committed two consecutive unforced forehand errors. The 28-year-old Russian then broke Oudin in the ninth game to take the set.
In a match marred by several unforced errors from both players, Dementieva made the decisive break in the sixth game of the decider with a forehand winner that hit the net before landing on her opponent's side. Dementieva closed out the match after two hours and 24 minutes with a backhand drop volley.
"I put pressure on myself because I know what I'm capable of," Oudin said. "I don't like losing at all. Losing is not good enough for me. I know people are hoping I'm the next up-and-coming American but I don't read any of that, the blogs, the press, what anyone says. I just focus on myself and I already have my own goals. That's what I'm concentrating on."
Safarova, who played in the final three years ago, lost her first set of the tournament but went on to post her second win in as many matches against Pennetta.
Pennetta saved two break points early in the first set and took her opponent's serve for a 4-3 lead, and then held with an ace.
Safarova saved one set point in the next game before Pennetta took the set in 37 minutes with her fifth ace of the match.
Both players traded serves twice early in the second set but Safarova went up 4-2 with another break and extended her lead to 5-2 before winning the set.
Safarova converted her only break point of the decider in the ninth game and served out the match at love.
"We both played very well and fought for every point, so I was very happy to win it," Safarova said. "It was about two or three points in the end."