Lalime has 35 shutouts in his career, but this was only the second one over the past three seasons.
The game's goal came from Jason Williams, lifting the Blackhawks to their sixth win in eight outings.
Ilya Bryzgalov made 24 saves for Phoenix, losers of three out of four.
The goal by Williams came on an odd bounce. Dave Bolland took possession of the puck in the corner and skated to the middle of the ice.
He suddenly spun and fired a shot that glanced off Williams' skate and past Bryzgalov at 7:58 of the opening period.
This was the fourth and final game between the teams this year, with Chicago having won three of them.
Lalime's most recent shutout came in his debut with Chicago in February, 2007.
2014: The Year in Music [PHOTOS]