"It's much more difficult playing someone who is over 30 (years-old) ... much more pressure for me because it's important that I'm the best over-30 player," joked the 34-year-old top seed.
"It was very important for me today to make sure he wasn't getting the confidence because when he has a litle bit of confidence he plays unbelievable, so I felt good about everything I did today."
The American top seed never allowed 32-year-old doubles specialist Bjorkman to find his rhythm in the opening set as he dictated the baseline rallies, rarely allowing the Swede to approach the net.
He broke Bjorkman's opening serve game for 2-0 and then broke to love for 5-1. Some careless play by the American allowed Bjorkman back to 5-3 but Agassi made no mistake in his next service game and he clinched the set 6-3.
Bjorkman looked like he had found his groove in the beginning of the next set as he became more aggressive and lifted his serving, but Agassi improved too and broke him in the fifth game and again in the seventh with some powerful returns to make it 5-2.
Bjorkman clawed his way back to 5-4 but Agassi clinched the match 6-4 on his first match point.
"Jonas is going to get his breaks of serve because he returns so well, I was just fortunate to be up two breaks of serve when I lost my serve in both sets. That made for a much easier day," said Agassi.
"To deal with Jonas the way I did today wasn't easy to do, so I have to feel good about many parts of my game for the match to go in straight sets."
Earlier in the day German fourth seed Tommy Haas needed just a break in each set to oust Dane Kenneth Carlsen 7-5, 7-5 to book his place in the quarters where he faces Belgian Olivier Rochus.
Swedish wildcard Michael Ryderstedt staged the biggest upset of the tournament so far when he beat Spanish fifth seed Feliciano Lopez 6-4, 6-7, 6-3.
Ryderstedt faces second seed Joachim Johansson in an all-Swedish quarter-final. Johansson outpowered American Jan-Michael Gambill 6-4, 6-4.
