And rather than allowing Thornton to muscle past him for a shot or a setup pass, Draper grabbed the Sharks star and took him out of the play by force.
Draper got a holding penalty, and Jonathan Cheechoo's resulting power-play goal sent San Jose to a victory and a 2-1 lead in its second-round series with the Red Wings. Game 4 is Wedneday night at the Shark Tank.
Yet even after committing the key penalty in the Sharks' comeback win, Draper couldn't say he would've done anything different against Thornton, whose grinding shifts and pinpoint playmaking have kept the Sharks ahead in two straight difficult playoff series.
"You just try to control him, but when you're playing against probably the best player in the league right now, he's going to find a way to get the puck to his guys," said Draper, a superb defensive forward who won the Selke Trophy in 2004. "When you're playing against Joe, you can't make mistakes against him. He's doing it all right now."
With 10 points in eight games, Thornton has been a monster force in a tight series, erasing any lingering notion his game recedes in the post-season. Last year's MVP is centring San Jose's top line, quarterbacking the power play and even double-shifting during important stretches.
On the day Thornton was left out of the three finalists for the Hart Trophy, the Red Wings affirmed that Thornton is more valuable than ever to the Sharks, who reached the 2004 Western Conference finals - a playoff round Thornton never visited during 7½ seasons in Boston before the Sharks acquired him last season.
"I think if anybody really had the answer, they would have shut him down, and we haven't found a way to do that yet," Detroit defenceman Chris Chelios said.
Thornton, who has a six-game scoring streak, led the NHL with 92 assists during the regular season - largely because it's almost impossible to steal the puck from him. He uses his six-foot-four frame to shield defenders, and he sees the ice with Gretzky-esque clairvoyance.
He has points on four of the Sharks' six goals against Detroit - not counting the penalty he drew to set the stage for Cheechoo's winner in Game 3. Coach Ron Wilson double-shifted him with several combinations of linemates to keep wearing down Detroit's defence.
"I want to get Joe out there more," Wilson said. "If he can dominate a game like that, I wouldn't be doing my job if I was playing him every four times. A lot of times he was going out every other shift (in Game 3). When the other team is worried about matchups, it ruins their rhythm. ... He loves to play, and he wants to be the difference-maker right now."
When Thornton was asked how much he could play if necessary, he laughed and said: "I don't know. Forty minutes? I have no idea."
Thornton played 23 minutes in Game 3, huffing with exhaustion every time he headed to the bench in the third period - yet Wilson is constantly amazed by Thornton's quick cardiovascular recovery.
Thornton might be the only person who sees nothing special in his play against the team long captained by retired centre Steve Yzerman, the inspiration for the No. 19 on his teal jersey.
"You get more comfortable when the game goes on, and being down 1-0, you get some extra energy," Thornton said. "Detroit is a good team, and they're not out of this series by any means. Both goaltenders are playing good, and both teams are really conscious about playing good defensive hockey."
Chelios wouldn't disclose whether the Red Wings have any new ideas on how to play Thornton, but Detroit captain Nicklas Lidstrom thinks they've just got to keep doing what they're doing - and hope it works soon.
"He's going to find ways to get his passes through," said Lidstrom, the four-time Norris Trophy who was named a finalist for the award again Tuesday. "We've got to find a way to take his time and spaces away. A lot of times you have one guy up on him, and another guy who's behind and ready to help out. You just have to try."