Rose, who makes his US residence in Orlando and lives a few minutes away from Bay Hill, looked as comfortable as if he was entertaining guests in his own living room, outshining his illustrious playing partners Woods and South African Ernie Els.
"I've got a good little support. I felt like the crowd was good to be me out there," Rose said after an opening round seven-under 65 gave him a two-shot lead.
"Obviously, Tiger is the man here at Bay Hill. He's won seven times but it's about what happens inside the ropes."
While Bay Hill has traditionally brought out the best in Woods, Rose says the presence of the 14-times Major winner has often brought out the best in his game. That was particularly true during a sunny but gusty opening round.
The 32-year-old world number five got off to a stuttering start with a bogey at the 11th but it was the only blemish in an otherwise sparkling round highlighted by an eagle at the par-five 16th and four straight birdies from the fourth.
"When you play with Tiger, you're sharp mentally," said Rose. "In the first round of the tournament it just elevates the day a little bit because he brings the crowd, he brings an atmosphere with him and I think that helps in a sense.
"It helps get you in the zone. He's always been the perfect playing partner.
"He's very complimentary out there and we always have a good time. Pretty much anybody who plays with him says the same."
Woods, who is a staggering 118-under par on Bay Hill's par fives for his career and seven-over on all the other holes, enjoyed Rose's company as well.
"Justin played a beautiful round of golf today," said Woods, who went five-under on Bay Hill's four par-fives on Friday. "He had every single facet of his game working, so we had a good time out there."