澳大利亞的Ajla Tomljanovic在當天的另一場女子四分之一決賽中對陣哈薩克斯坦的17號種子Elena Rybakina。
弗里茨正在參加他的第一個大滿貫四分之一決賽，他以6-3 6-1 6-4戰勝了澳大利亞的傑森-庫布勒，進入了這個階段。
澳大利亞人正在享受他在SW19的最佳表現，因為八年前的首次出場，並相信他有一個 "機會"，對陣世界排名第43位的加林，他在上一輪讓澳大利亞的前景Alex de Minaur吃驚。
Rafael Nadal will face the toughest challenge of his Wimbledon campaign so far when he takes on American 11th seed Taylor Fritz on Wednesday.
A potential semi-final awaits against Australian Nick Kyrgios, who faces Chile's Cristian Garin on day 10.
Romania's Halep, the 16th seed, will face 20th seed Anisimova on Centre Court from 13:30 BST, with their match followed by Nadal versus Fritz.
"I did not think about [not dropping a set] until now but day by day it is better and better," said Halep, who is yet to be taken to a decider this championships.
"I am just looking forward to playing the next one and giving my best."
Australia's Ajla Tomljanovic takes on Kazakhstan's 17th seed Elena Rybakina in the day's other women's quarter-final.
This will be Nadal's first appearance in the quarter-finals at the All England Club in three years after Covid meant the 2020 edition was cancelled and injury saw the 36-year-old miss out last year.
But the 22-time Grand Slam champion will come up against a player who has already got the better of him this year.
Fritz is playing in his first major quarter-final, having reached this stage with a 6-3 6-1 6-4 win over Jason Kubler of Australia.
And the 24-year-old will be full of confidence after beating Nadal to claim his first Masters 1000 title in the Indian Wells final earlier this year.
"In a personal way, for me to be able to be in quarter-finals after three years it's amazing for me so very, very happy," said Nadal.
"Every match is different. He is playing well and having a very good year including a first Masters 1000 title, against me by the way.
"But we will be in the quarter-final of Wimbledon, so what will I expect."
Kyrgios beat Nadal on his Wimbledon debut in 2014, when he reached the quarter-finals, and will face the Spaniard in the semi-final if both players come through their last-eight ties.
The Australian is enjoying his best run at SW19 since that inaugural outing eight years ago and believes he has an "opportunity" to progress against world number 43 Garin, who surprised Australian prospect Alex de Minaur in the previous round.
"I was expecting to play Alex," said Kyrgios. "Then when I walked off the court and I got told it was Garin. It was surprising. I look at it as an opportunity but I need to do so many things before that match to get ready."
Garin saved two match points during that victory over De Minaur and says he thinks Kyrgios' world ranking of 40th does not do the 27-year-old's ability justice.
"Nick is very good player. For me, maybe the best serve on tour," he said. "I think Nick has to be seeded because he for me is one of the best players on the tour and on grass, obviously."
The match comes a day after it emerged Kyrgios is set to appear in court in Australia next month in relation to a claim of common assault. • None Alerts: Get tennis news sent to your phone
Kyrgios has forged a reputation as one of his sport's biggest wasted talents, but Australian doubles great Todd Woodbridge says his compatriot has applied himself more than ever to be ready for this Grand Slam.
"Nick has prepared the best ever for a tournament here," he told the BBC.
"He spent time at home. He went to the Hunter's Hill tennis Club in Sydney with Lleyton Hewitt coming into winter and the courts were not that good but he put in a really big effort and his press conferences throughout the tournament were good."
Kyrgios reached two semi-finals at grass events in the lead-up to Wimbledon and enjoyed his first taste of Grand Slam success when he partnered countryman Thanasi Kokkinakis to the men's doubles title at the Australian Open in January.
"There was a time where I was having to be forced out of a pub at 4am to play Nadal [in the] second round," said Kyrgios, speaking before Tuesday's allegations. "I've come a long way, that's for sure.
"But I think just daily habits and the people around me. I've got an incredible support crew. My physio is one of my best friends. My best friend is my agent. I've got the best girlfriend in the world. I've just got so many people around me, they just support me. I feel like I can reflect on all those dark times when I pushed them all away.
"Now to sit here quarter-finals of Wimbledon, feeling good, feeling composed, feeling mature, having that around me, I'm extremely blessed. I feel like I'm just comfortable in my own skin."