BETHESDA, Md.—It’s not often that a player is bold enough to challenge Tiger Woods on the golf course. Rarer still is when it happens during a pro-am round from one of his amateur partners.

“That still puts me 1 up,” Dallas Cowboys quarterback Tony Romo said to him Wednesday morning.

“Does it, now?” Woods replied, not sounding the least bit concerned.

The world’s No. 1 player then smoked a fairway metal down the 17th at Congressional Country Club. Romo, a scratch player who asked to play from the championship tees, followed with a 3-wood that traveled about ...

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