An out-of-sorts Woods was four-over-par with four holes remaining when play was halted after a difficult, damp and overcast day at Augusta National, one of 18 players yet to complete their opening rounds in the year's first major.
The 23-year-old Rose, competing at Augusta for the second time, fired a five-under-par 67 in the third group out, finishing two strokes clear of 50-year-old Jay Haas and his fellow American Chris DiMarco, who aced the 180-yard sixth hole.
"That was a dream start," Rose told reporters. "Any time you shoot a round that could be the round of the day in a major, it has to be one of the best rounds you've ever played."
Out on the course, triple major winner Ernie Els was in touch with the lead at two-under after 17 holes, level with Germany's Alex Cejka, also after 17.
"It was a weird day," said South African Els, who has finished no worse than tied for sixth in his last four starts at Augusta.
"It was a little difficult. Nobody got into a rhythm.
World number one Woods, bidding for a third Masters title in four years, had teed off in the penultimate group and was battling after 14 holes, a double-bogey at the par-four fifth sandwiched by dropped shots at the first and eighth.
No better was defending champion Mike Weir of Canada, an up-and-down display leaving him at four-over after 15 holes.
"I didn't play well," said Weir, who became the first left-hander to win a major in 40 years at Augusta last April.
"I wasn't sharp and wasn't driving well. It played tough."
Englishman Rose, who took the golfing world by storm when tying for fourth as an amateur at the 1998 British Open, launched his round in dramatic fashion, holing a 25-foot birdie putt at the difficult 435-yard first.
Rose then picked up further strokes at the par-five second and the 460-yard ninth to reach the turn in three-under 33.
Although he three-putted the par-four 11th for his only bogey of the day, he hit back with birdies at 17 and the last to set the early pace.
"It all stemmed from my first tee shot," said Rose, the youngest professional in the event. "I crashed it straight down the middle and, from that moment on, felt really comfortable on the golf course."
Haas, who is determined to play his way on to the U.S. Ryder Cup team for this September's showdown with Europe at Oakland Hills in Detroit, was delighted with his round.
"I played extremely well, drove the ball well, hit a lot of good iron shots and made some nice putts," he said.
"I'd love to try to get into the hunt on the weekend and over the last nine holes. I definitely think someone aged 50 can win here at Augusta."
Fiji's Vijay Singh, the 2000 champion, and former world number two Phil Mickelson of the U.S. both got to two-under with four holes to play before tumbling down the leaderboard.
Singh ran up a triple-bogey eight at the 500-yard 15th before dropping more shots at 17 and 18 for a 75. Mickelson double-bogeyed the par-three 16th on his way to a level-par 72.
The 2004 Masters promises to be one of the most open in recent memory, with the focus on whether Woods can break a barren run of failing to win in his last six majors and on how much his rivals have closed the gap.
Established challengers such as Singh, Els, Mickelson and Davis Love III have all displayed superb form in recent months.
Much was also expected of Australia's Adam Scott and American Chad Campbell over the fast-running Augusta layout, which was baked by eight days of unbroken sunshine before Thursday's intermittent showers.
Four-times winner Arnold Palmer is certain to provide the week's most nostalgic moment in his record 50th and final U.S. Masters. The 74-year-old American, who has not made the cut at Augusta since 1983, opened with a 12-over 84.