The 22-year-old Serb, who is trying to win her second claycourt title of the season after her success in Charleston last month, dragged her Russian opponent round the court with angled groundstrokes.
"I was a little bit nervous at the start but then I got into a rhythm, started to control the points, play aggressively, and that was the key," said Jankovic.
Enjoying her best claycourt season on the circuit, Jankovic has also reached the quarter-finals in Amelia Island, the semi-finals in Warsaw, and the last eight in the German Open.
"I used to think that I didn't like clay. I wasn't used to it and I didn't know how to slide," she said.
"Then I worked with a Spanish coach, I learned how to slide and I got a lot of confidence, especially after Charleston. I'm starting to like it out there."
After an early exchange of breaks, Jankovic took control by breaking in the sixth game and then again in the eighth, chasing down a drop shot to stroke a forehand winner down the line to take the first set in 35 minutes.
She continued to dominate in the second set, holding off break points in the opening game, before whipping a backhand past her rival to break in the second game. She went 4-0 up when her opponent double-faulted on break point.
Tenth seed Dementieva, who finished runner-up at Roland Garros in 2004, pulled one break back, but Jankovic rallied to restore her two-break cushion in the following game before holding serve to close out the contest.
In the semi-final she will face either 2002 champion Serena Williams or 14th seed Patty Schnyder.