Henrik Zetterberg added a goal and three assists, and Dan Cleary got the other goal for Detroit. Nicklas Lidstrom had three assists, and Dominik Hasek stopped 24 shots.
Lee Stempniak, Ryan Johnson and Keith Tkachuk scored for St. Louis. Manny Legace made 24 saves.
Draper knocked Lidstrom's pass, which was tipped by Stempniak, out of the air and into the net with 6:29 left to finish off a 2-on-1 break. Cleary was in the penalty box for goaltender interference.
Cleary added his 20th goal into an empty net with 28 seconds left.
Tkachuk tied it at 3 with his 16th goal 9:56 into the third period.
Holmstrom's second goal of the game had given Detroit the lead just 2:14 earlier. He scored his 18th goal on a breakaway.
Johnson tied the game at 2 with 5:19 left in the second period. He sent a pass from Dallas Drake under Hasek. Drake had stolen the puck from Pavel Datsyuk just inside the St. Louis blue line.
'CANES go to WASHINGTON: President Bush congratulated the Carolina Hurricanes on their 2006 Stanley Cup championship and ribbed the team about their broken noses, among other things, at the White House on Friday.
"They're obviously great athletes. All you got to do is look at their noses," Bush said. Carolina team captain Rod Brind'Amour grinned and touched his nose, and the audience laughed.
"Appreciate you putting your false teeth in," Bush then quipped.
The team, which ranked 28th out of 30 teams at the start of last season, beat the Edmonton Oilers in June to win the Stanley Cup - proudly displayed in the East Room for an audience of about 250 people.
"I'm not sure which is prettier - the Stanley Cup, or Mike Commodore's hair," Bush said, referring to the defenseman whose recently shorn mop of red hair attracted a fan following when he played for the Calgary Flames.
Bush, known as a baseball fan, told the team, "it's a pretty big deal for a guy that doesn't know how to ice skate" to welcome them to the White House.
He commended them for their determination and for charity work off the ice, saying "they bring class to their profession." Team members took the Cup on visits to children's hospitals and the Wounded Warriors Barracks at Camp Lejeune, N.C.