The Blues scored two power-play goals in a game for just the second time this season. They broke out of an 0-for-9 slump but still have a league-low 14 goals with the man advantage.
Arnott pushed the lead to 3-1 on a power-play goal with 1.1 seconds left in the second period. Arnott, who has eight goals, scored for the fourth time in the last five games after just four goals in his first 29 games.
Grachev scored his first career goal at 6:45 of the third period to push the lead to 4-1.
Dallas rallied with goals from Eric Nystrom and Michael Ryder. Ryder cut the deficit to 4-3 with his 14th goal of the season with 5:13 remaining.
But Stewart scored an empty-netter with 50 seconds left to push the lead to 5-3.
Hitchcock was pleased with his team's effort especially the season-best two-for-two performance on the power play.
"We played really hard and did a lot of good things," Hitchcock said. "We really dialed it up today. We were firing from everywhere."
Cracknell was recalled to replace center T.J. Oshie, who will miss at least two games with an injured left wrist. Cracknell whipped a wrist shot past Dallas goalie Richard Bachman from a sharp angle to give St. Louis the lead for good 2-1.
"I just moved my feet and tried to catch him off guard and it worked," Cracknell said. "I saw it trickling in, Once it crossed that goal line, I was very happy."
St. Louis winger David Perron, who added a pair of assists, was impressed with Cracknell's first-game contribution.
"Guys like him need to step up and he did a good job of doing just that," Perron said. "We've always got guys like him that can do the job."
St. Louis goalie Jaroslav Halak made 20 saves to improve to 7-7-4 after a 1-6 start to the season.
The Stars, who were outshot 38-23, fell to 12-3-1 when scoring in the final ten minutes of regulation.
Bachman dropped to 5-3. He let in a pair of goals from bad angles including Stewart's first-period tally that put the Blues in front 1-0.
"There's no question, a couple of those goals, he would like to have back," Dallas coach Glen Gulutzan said. "But we just needed to put more pucks on the net."
Nystrom, who brought his team to 4-2 with his 12th goal of the season at 7:57 of the third period, said the Stars' poor special teams performance was the difference.
"We've been giving up too many goals on the PK (penalty kill) lately," Nystrom said. "We were coming back, but they played hard and they had that extra edge tonight."
The Stars' No. 1 goalie, Kari Lehtonen, is expected to return to the lineup this week. He has not played since injuring his groin on Nov. 26.
"He's skated the last few days and he's very close," Gulutzan said. "I wouldn't be surprised to see him against Columbus (Thursday).
Oshie will not play Tuesday at Detroit but is expected back Friday against Nashville. ... The Blues have given up a league-low 19 goals in the first period. ... Hitchcock guided the Stars to the Stanley Cup in 1999. ... Dallas LW Loui Eriksson has three goals and three assists in his last six games against St. Louis. The Stars are 2-11 when trailing after two periods. ... Stewart had a game-high seven shots on goal.