Crawford had appeared in just eight games over three seasons for the Blackhawks prior to the current campaign and he improved his record to 21-12.
Chicago celebrated the return to the bench of Coach Joel Quenneville, who had missed four games due to a bleeding ulcer.
Tomas Kopecky gave Chicago the lead on a slap shot with 2:48 to go in the first period and it remained a 1-0 game until Marian Hossa scored 2:35 into the third.
Patrick Sharp added an empty-net goal with 31 seconds to play.
Chicago has won three in a row and four out of five. Pekka Rinne stopped 24 shots for Nashville, which has lost three straight.