Haas dispatched big-serving American Sam Querrey 6-4, 7-5 while Blake completed his 200th career match victory with a 6-1, 6-3 demolition of compatriot Scoville Jenkins.
Belgian third-seed Xavier Malisse, the 2005 champion and runner-up to Haas last year, also advanced to the last eight despite losing his second match 6-7, 7-6, 6-3 to Germany's Rainer Schuettler.
Malisse, who beat Colombia's Alejandro Falla in his opening encounter on Tuesday, scraped through his round-robin group based on tiebreakers.
Second-seeded Haas, who shrugged off jet lag and a slow start to win his tournament opener the previous day, held serve throughout against the 19-year-old Querrey.
The German, who had a fine run to the semi-finals of the Australian Open last week, completed his seventh victory at Delray Beach in seven matches.
"It was a quick turnaround after finishing late last night, but I got in a good night's sleep," said the 28-year-old, who lost to Chile's Fernando Gonzalez in the Australian Open semi-finals six days ago.
QUITE WINDY
"I'm feeling better but it was quite windy out there and it's tough to prepare yourself for a day like this. You just have to try and adjust when you're out there."
World number five Blake, who clinched his ninth ATP title in Sydney earlier this month before losing in the fourth round of the Australian Open, lost just two points on his first serve as he crushed Jenkins in 51 minutes.
Blake did not face a single break point in sealing a quarter-final berth by winning his two matches in the ATP's new round-robin tournament format.
He joined compatriot Vince Spadea, fourth seed Benjamin Becker of Germany and Italy's Davide Sanguinetti in the last eight.
Becker brushed aside American Jesse Levine 6-3 6-3 while ATP Tour veteran and eighth seed Spadea, who lives in nearby Boca Raton, beat compatriot Ryan Sweeting 7-5 6-4.
Sanguinetti, the 2002 champion, edged past big-serving Amer Delic of the U.S. 6-3, 4-6, 6-3.
