Nolan, out of the NHL since the 2003-04 season, scored one of Phoenix's three goals in the third period.
Mike Comrie and Mike Zigomanis also scored in the third period to put the game out of reach. Nolan made it 4-2 with just over five minutes left and about 12 minutes after Comrie scored the game's only power-play goal. Zigomanis notched his first of the season in the final minute.
Dave Scatchard and Shane Doan also scored for the Coyotes, who matched their total scoring output from the previous four games.
Radek Dvorak scored his second of the season and Martin Rucinsky netted his third for the Blues, who played in front of a sparse crowd of 8,531.
The attendance was held down because of the St. Louis Cardinals' home playoff baseball game.
The Coyotes (2-4) had reached three in a game only twice before in the first five contests, but avoided their worst start since moving to Phoenix 10 years ago. After winning their season opener, the Coyotes dropped four straight.
Phoenix began last season with five losses and three points in its first six games, the worst opening since the franchise relocated from Winnipeg. In the last season as the Winnipeg Jets, they earned only one victory and four points in eight games.
Notes: The Blues' 27 shots were their fewest in six games this season. ... The loudest cheers came when replays were shown of the Cardinals scoring runs in Game 5 of the NL championship series against the New York Mets.