Russell, trailing 5-2 in the first set, had the trainer on the court to work on his leg.
Besides for having to save one break point in the fourth game of the first set, Querrey played confident tennis throughout the 44 minutes he was on the court.
"I thought that was the best attitude I've had all year," Querrey said. "It's the most aggressive I've been all year.
"I was hitting second serve returns and taking cracks at them, and dominating with my forehand. It felt great."
The biggest upset came from 62nd-ranked Ivan Dodig of Croatia, who beat fifth-seeded Alexandr Dolgopolov of the Ukraine 6-3, 6-3.
Dolgopolov, who reached the Memphis quarterfinals last week, initially led 3-0 in the match.
From there, Dodig, a quarterfinalist here in 2011, reeled off nine straight games for a 6-3, 3-0 lead in the 57-minute match.
"It was a little bit strange. Coming from indoor to first tournament outdoor, every player is struggling a bit.
"First few games I was struggling, but I know he's had some problems with his back."
Eighth-seeded Xavier Malisse of Belgium, a two-time past champion here, won his first-round match over Alejandro Falla of Colombia 6-3, 6-3.
The 50th-ranked Malisse, who has reached the quarterfinals at the Auckland and San Jose tournaments this year, has beaten the 59th-ranked Falla all four times they've played.
Malisse has a 26-10 record at this tournament.
The 109th-ranked Ernests Gulbis of Latvia is the 2010 Delray Beach champion. This year, Gulbis has had to come through qualifying to reach the main draw this year.
Gulbis defeated Denys Molchanov of the Ukraine 6-7 (4), 7-5, 6-4 to qualify on Monday.