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Roddick, the fourth seed, converted all three of his break chances to book his second quarter-final appearance of the season with a 6-4, 7-5 victory.
Istomin had beaten Roddick in the quarters en route to the final at San Jose, California, in February, before falling to Canadian Milos Raonic in the title match.
"We played a few weeks ago, and it was pretty ugly," Roddick said. "He took care of me pretty easily, so it’s nice to get one back. I'm happy to get through."
Roddick said he has plenty of things to work on, but he's seeing progress in his game.
"I served horrendously and still won, was still able to break serve," he said. "Returning is getting a little better."
Roddick, 29, next faces seventh-seeded South African Kevin Anderson.
Anderson took his 2012 record to 7-4 with a 6-3, 3-6, 6-3 victory over two-time former Delray Beach champion Xavier Malisse of Belgium.
Fifth-seeded German Philipp Kohlschreiber reached the quarter-finals with a 6-2, 6-2 win over Croatian Ivan Dodig, breaking him twice in each set to secure victory in 78 minutes.
In his match against Israel's Dudi Sela, who beat Finland's Jarkko Nieminen 6-4, 6-4, Kohlschreiber will be aiming for his third semi-final of the season, after making the last four in Auckland and Montpellier.
In the other quarter-finals decided on Wednesday, top-seeded American John Isner faces eighth-seeded Australian Bernard Tomic and former champion Ernests Gulbis of Latvia will play Australian qualifier Marinko Matosevic.
