The British No 2 was pushed hard in the first set by the 12th-seeded Dane before prevailing in a tie-break on Thursday evening . He then raced into a 4-0 lead in the second set and went through 7-6, 6-2.
Rusedski, seeded No 7, arrived at this tournament in good heart after recently retaining his Hall of Fame Championships title in Newport, Rhode Island.
The 31-year-old has a good record in Indianapolis, having beaten Felix Mantilla in the 2002 final.
Rusedski said: "I was pleased with the way I played and I dominated the first set even though it went to a tie-break. Then I went up 4-0 in the second set and got aggressive. It's a great start to the American summer and this has always been a good part of the year for me."
The left-hander now plays the second-seeded German Nicolas Kiefer, who beat the unseeded American Kevin Kim 6-1, 6-3. Rusedski holds a 5-4 career advantage over Kiefer but was thrashed 6-1, 6-4 when facing the 28-year-old for the first time in five years last July.
"I have to play my own game and come to the net and be aggressive," Rusedski said. "He beat me last time in Los Angeles but I feel fresher now."
The top-seeded American Andy Roddick cruised into the quarter-finals with a routine 6-2, 6-2 win over the Israeli Noam Okun.
Roddick, who is looking for his third successive title in Indianapolis, plays Robby Ginepri in the quarter-finals after his his compatriot unexpectedly beat Paradorn Srichaphan, of Thailand, 6-0, 6-4 in only 46 minutes.
In Stuttgart, Rafael Nadal continued his progress at the Mercedes Cup yesterday, beating Tomas Zib 6-2, 6-1 to reach the semi-finals. The Spaniard's 32nd successive match win on clay saw the French Open champion through to face Jarkko Nieminen in the last four, after the unseeded Finn beat Andreas Seppi, of Italy, 6-2, 6-3.
Nadal has been untouchable this week and the result looked a foregone conclusion from the first game.