Defending champion Tom Watson was one shot off the pace at 1-under-par 69. He finished alongside 2002 Tradition champion Jim Thorpe, Wayne Levi and Fuzzy Zoeller.
Rains drenched the long South course at Firestone Country Club as the second major of the Senior Tour season got under way.
'It is very, very wet,' said Kite, who is seeking his second major victory on the Senior Tour.
Kite got off to a quick start at the par-5 second after he knocked his 5-wood within 40 feet of the cup to get on the green in two. The 52-year-old two-putted for birdie to get into the red.
At the sixth, Kite hit a 9-iron six feet from the hole and birdied to reach 2-under. However, it was Morris Hatalsky who took the early lead.
Hatalsky played the back side first and opened with a birdie at the 12th. He reached 3-under with back-to-back birdies from the 14th to briefly hold the lead before running into trouble with a bogey at No. 16. Hatalsky's problems continued as he collected four more bogeys for a round of 2-over 72.
Kite found misfortune at the seventh after he pulled a 5-iron into the left bunker and failed to get up and down. He recovered on the inward nine and landed a pitching wedge inside 18 feet of the hole for birdie at the 14th as he closed out his round at minus 2.
'Everybody has their opinion as for how difficult the golf course is,' said Kite, who has won twice already in 2002. 'This is a major championship, last I checked, and major championships are supposed to be more difficult than your normal event.'
Goin grabbed a share of the lead late in his round. At the closing hole, he hit his approach within eight feet to set up the last of a stretch of three straight birdies to finish at 2-under.
'There is a long way to go,' said Goin, who has yet to win on tour. 'It's always nice to get off to a good start. I haven't been playing well lately, for one particular reason or another. The rhythm kind of came around today.'
Smith, who is also seeking his first win on the Senior Tour, first moved into a tie for the lead with a birdie at the 11th. However, the 51-year-old ran into trouble with a bogey at very next hole.
Smith countered with a birdie at the seventh only to drop a shot with another bogey at the eighth. He remained calm and finished his round on a positive note with a birdie at the ninth.
'It's the best round I have had in quite a long time. I played real solid,' said Smith.
The leaders' opening-round score was the highest at this event since Chi Chi Rodriguez stood atop the leaderboard with a 2-under 70 after the first round in 1987.
Watson collected four birdies and three bogeys on his round to finish one stroke off the pace in the opening round of his title defense. The 52-year-old was at 1-over through 11 holes but was able to right the ship with back-to-back birdies from the 12th.
'I felt I was swinging well, I was just a little bit off,' said Watson. 'All in all it was a good round.'
Doug Tewell, who won this tournament in 2000, was part of a large group at even-par 70. He was joined by Brian Lowe, Bobby Wadkins, Walter Hall, Jim Ahern, Jerry Tucker, Larry Nelson, Bruce Fleisher, Larry Ziegler, Jay Overton and Roy Vucinich.
Jack Nicklaus, who missed this year's Masters because of a bad back, had some of the best shots during the opening round to finish one stroke further back at 1-over-par 71.
Nicklaus made his first birdie of the day at the par-4 11th after his approach found a greenside bunker. The 62-year-old blasted out of the sand and watched as the ball rolled into the cup.
At the par-4 17th, Nicklaus was on the green in two but had 50 feet for birdie. He ran home the long, bending putt for his second birdie of the day to the delight of the gallery.
Another bright moment of a dreary day was the play of 80-year-old Jack Fleck, who posted a 7-over-par 77.
'Well, I was very fortunate outside the 18th hole, but it was probably the finest round of putting that I may have had in my lifetime,' said Fleck, who ousted Ben Hogan in a playoff to win the 1955 U.S. Open.
Full-field scores from the Senior PGA Championship