"He felt fine after [Saturday], which was the most important thing," coach Joel Quenneville said Sunday. "Today was the same as yesterday, so we feel he's turned the big corner there and is heading in the right direction."
Crawford has been out with an upper-body injury since March 16, and missed his ninth consecutive game Sunday.
Chicago has four games left before the playoffs.
Forward Andrew Shaw missed Sunday's game against the Bruins with an upper-body injury that he suffered Friday against Winnipeg. Quenneville said he will also sit out Tuesday against Arizona, but he expects him back on the ice before the end of the regular season.
Before Sunday's game against the Bruins, Crawford skated and took practice shots from goaltending coach Jimmy Waite for the second straight day.
Crawford has a career-high 35 wins this season, along with 2.32 goals against average and .926 save percentage that rank him among league leaders.