The victory, in just 76 minutes, was the 14th in a row for the fourth-seeded Russian, who won the Auckland and Sydney tournaments before arriving at Melbourne Park.
She is unbeaten in 2009 and plays Spain's unseeded Carla Suarez Navarro in the last eight. Navarro continued her roller-coaster run at the Australian Open with a 6-3, 6-2 fourth-round victory over compatriot Anabel Medina Garrigues
It is the first time Dementieva has made the Australian Open quarter-finals, where she will be joined by three other Russians, headed by third seed Dinara Safina.
"Dinara looks like she's in a good shape," Dementieva told reporters when asked on whether she was a favourite for the Daphne Akhurst Memorial Cup.
"She's made the biggest improvement since last year, so she's probably the favorite to win.
"But there is still Serena (Williams) and there are a lot of good players here. It's going to be a tough competition.
"I mean, I'm not thinking who's the favorite; I'm just trying to take one match at a time and be focused and play my best."
Dementieva had initially complained after her first round win at Melbourne Park that she was feeling the affects of so many matches, though on Monday the Russian said she was now pleased to have played both warm-up tournaments.
"I think it was the right decision to come to Auckland and play a smaller tournament in the beginning just to get confidence and just to play some matches there.
"I mean, it just feels good so far."
Dementieva had a nervous start against the 18th seeded Cibulkova when she suffered an early break.
After breaking the Slovak to take a 3-2 first set lead, however, she rattled off nine straight games and was serving for the match before Cibulkova broke to delay the inevitable for 10 minutes.
The Russian sealed victory with a backhand winner on her third match point.
"I think it was a good match, you know, very solid game from the beginning till the end.
"I'm just very satisfied with the way I was playing."
Suarez Navarro continues dream run
Diminutive Spaniard Carla Suarez Navarro continued her roller-coaster run at the Australian Open with a 6-3 6-2 fourth-round victory over compatriot Anabel Medina Garrigues on Monday.
Suarez Navarro, who came from behind to upset sixth seed Venus Williams in the second round, was barely troubled, sealing victory in just 73 minutes with a forehand winner down the line after working Medina Garrigues around the court.
The 20-year-old, who stands just 1.62 metres tall, used her strong backhand to help blast 20 clear winners and capitalised on four of her five break opportunities.
She will play Russian fourth-seed Elena Dementieva in Wednesday's quarter-finals.
"I think the next round is a very difficult match," Suarez Navarro said, speaking through an interpreter. "Dementieva is a very good player, it will be very difficult."
Suarez Navarro, who speaks only a few words of English, is one of two unseeded women through to the last eight, along with Australian Jelena Dokic, but her progress is no real surprise although she is only playing in her fourth grand slam event.
She burst onto the scene at last year's French Open when she made the quarter-finals, beating former world number one Amelie Mauresmo and Italian Flavia Pennetta along the way.
Dementieva said she was impressed by Suarez Navarro the first time she saw her play and was not the least surprised by her progress at Melbourne Park.
"I was watching her playing French Open last year when she qualified and played in the quarters beating Amelie Mauresmo," Dementieva said.
"I think she's got a lot of talent, and she's physically very fit. So, no, I'm not surprised to be facing her."
Raised in the Canary Islands, Suarez Navarro did not start playing tennis until she was nine, encouraged to take up the sport by her mother, a former gymnast who worked as a teacher.
Suarez Navarro turned professional in 2003 and spent the first four years playing lower-level ITF events, but her career did not take off until she left home to join a tennis academy in Barcelona.
The following year she came through the qualifiers at the French Open and made the last eight, losing to current world number one Jelena Jankovic.
She made such an impression that she was given a wildcard entry to Wimbledon, where she was beaten in the second round, again by Jankovic.
She was picked for the Spanish team that made the Fed Cup final and made her Olympic debut at Beijing, before losing in the first round at the U.S. Open.
Suarez Navarro finished 2008 ranked 50th in the world but is poised to go much higher after her great start in Australia and believes her experience in Paris last year will benefit her.
"It's different because it's the second time, it's not the first time," she said. "I think I can play better than the first time with Jankovic in Roland Garros."
Kuznetsova strolls into quarters
Russia's Svetlana Kuznetsova got an easy ride into the quarter-finals when her fourth-round opponent retired hurt.
Kuznetsova was leading Zheng Jie 4-1 in the first set when the Chinese pulled out because of a wrist injury.
Kuznetsova, a former U.S. Open champion seeded eighth at Melbourne Park, is the fourth Russian woman through to the last eight, joining Dinara Safina, Elena Dementieva and Vera Zvonareva.
Kuznetsova's quarter-final opponent will be Serena Williams.
Serena advances after ill Azarenka retires
Serena Williams was gifted a place in the quarter-finals when the American's fourth-round opponent Victoria Azarenka succumbed to a mystery virus.
Azarenka, from Belarus, was leading 6-3, 2-4 when the 13th seed was forced to retire as the effects of the virus sapped her energy completely.
The 19-year-old almost fainted as she started feeling dizzy and struggled to maintain her balance.
She took a medical break after almost vomiting into her hands and tried to keep out of the sun by stumbling into the shade at the end of each point.
"I started feeling really sick in the morning, I woke up at 6 a.m. and I was throwing up all morning. I just felt so weak," Azarenka told reporters.
"Once I got to the court, I went to see the doctor, I felt a little bit better. Throughout the first set, a little bit of the second, then I just had no more energy to go."