The No.4-seeded Safarova dropped 15 aces on Tomljanovic and fought off all seven break points she faced in the match en route to a 7-6(4), 6-2 victory over the similarly-big-serving WTA Rising Star.
"It was a good match for me," Safarova said. "I was serving really well in both sets. It was a really close set in the first set - the tie-break too - and I'm really happy I got through my first round."
She's now through to her fifth quarterfinal of the year, all five of them coming at Premier-level events or higher - Sydney, Charleston, Wimbledon, Tokyo [Pan Pacific] and now right here in Moscow.
Awaiting Safarova in the quarterfinals will be the No.5 seed, Kuznetsova, who needed two hours and 41 minutes to get by Ukrainian qualifier Kateryna Kozlova, 3-6, 6-3, 6-3. After dropping the first set Kuznetsova went right to work, breaking early in the second and third sets en route to victory.
Kuznetsova leads Safarova in their head-to-head series, 4-3, and she did win their only previous meeting this year as well, in the fourth round of the French Open. They're 3-3 on hardcourts though.
The only other early winner on Day 2 of the Premier-level event was Alison Riske, who carried her winning momentum from Tianjin to Moscow with a 6-1, 6-2 win over Russian wildcard Darya Kasatkina.
Riske won the first WTA title of her career at the Tianjin Open last week. Having never been to a WTA final before she didn't lose a set all week, holding off Belinda Bencic in straights in the final.
But back to Safarova - could one of the reasons she's surging up the rankings this year be the strengthening coaching partnership she has with Canadian coach Rob Steckley? Here's a bit on him...