In her fifth straight semifinal here, Dementieva will play Dinara Safina, who beat Vera Zvonareva 6-2, 3-6, 6-3.
In the men's quarterfinals, Janko Tipsarevic of Serbia beat Radek Stepanek of the Czech Republic 6-4, 3-6, 6-3.
Dementieva, runner-up in 2001 and 2004, prevailed on a first-set tiebreaker and won four consecutive games in the second to win in 1 hour, 28 minutes. She served five aces.
The 18-year-old Azarenka, who upset second-seeded Maria Sharapova in the second round, never threatened Dementieva.
Safina, sister of Marat Safin, easily won the first set and was level at 3-3 in the second before losing three straight games. The 17th-ranked Russian broke twice in the third set to advance to her second semifinal in her hometown. She lost to eventual champion Mary Pierce in 2005.
Safina upset Martina Hingis in the final of the Australian Women's Hardcourt in January for her fifth career title.
Serena Williams was scheduled to play eighth-seeded Nicole Vaidisova of the Czech Republic in a later quarterfinal.
Williams, an eight-time Grand Slam champion, is playing in Moscow for the first time in a decade. In 1997, the 16-year-old Williams qualified and lost in the first round when she was ranked 448th.