Roddick, who has dropped to 30th in the world rankings, defeated Denis Istomin 6-4, 7-5 and, for the first time this season, has won two matches in the same event.
Istomin surprised Roddick two weeks ago in California but converted just one of five break chances in their rematch.
Roddick will take on Ryan Anderson in the quarterfinals after Anderson defeated five-time Delray Beach finalist Xavier Malisse 6-3, 3-6, 6-3.
In the other second-round matches contested Thursday, Philipp Kohlschreiber breezed by Ivan Dodig 6-2, 6-2 and Dudi Sela was a 6-4, 6-4 winner over Jarkko Nieminen. Kohlschreiber and Sela will meet in Friday's quarterfinals.
The other quarterfinal matchups, which were determined Wednesday, will send qualifier Marinko Matosevic against Ernest Gulbis and No. 1 seed John Isner against Bernard Tomic.
2014: The Year in Fashion [PHOTOS]
UPI Sports Results for September 19, 2014