Tim Henman and Arvind Parmar made progress at the Rotterdam Open on Wednesday but fellow Briton Greg Rusedski crashed out.
Henman made the quarter-finals in Rotterdam last year
Henman had an impressive 6-4 6-4 first-round win over Thomas Johansson and next meets Novak Djokovic.
Parmar maintained his superb form to beat Germany's Dominik Meffert 6-3 6-3 in round two and he will Christophe Rochus in the last eight.
Top seed Nikolay Davydenko saw off Rusedski 6-4 6-1.
"He just got better," said Rusedski, who let an early lead slip and then decided not to serve and volley in the second set.
"It was indecision, I didn't know what to do. I just didn't have too many options out there."
Parmar, the world number 230, came into the tournament as a lucky loser after losing to Meffert in qualifying.
"I'm thrilled, it's been a while since I've been in the quarter-finals of a tour event," Parmar told BBC Five Live.
"I'm really happy I'm playing well over the last couple of days and it's been a successful tournament so far."
And Parmar admitted he had been inspired by watching fellow Briton Andy Murray beat Andy Roddick and Lleyton Hewitt on his way to winning the San Jose title last week.
"You see it all the time from different players from different countries," he said. "It takes one or two guys to do well and it has a knock-on effect.
"I don't know what it's down to, it's just subconscious. You see Andy doing it and you think 'why can't it be me?'
"Seeing Murray play great tennis, beating guys in the top 10 and taking home tournaments is a great boost for everyone who knows him and are good friends with him."
Henman was delighted to beat world number 13 Johansson after struggling with a back problem in recent weeks.
"I played aggressively and took my chances," he said. "I guess most importantly I felt physically good out on court.
"I've had an ongoing back issue for quite some time, probably nearly 18 months, and it's sometimes a bit unpredictable.
"It was very bad in Marseille last week, I was there ready to play but my back thought otherwise, so I was still a little bit unsure whether I was going to play this week. I was pleased with the whole performance tonight."
In other matches, Finland's Jarkko Nieminen was a surprise 7-5 7-6 (7-5) winner over fifth seed Mario Ancic of Croatia.