Defending champion Noboru Sugai heads a group of seven players tied one shot behind the leaders. Also is that group are Carl Mason, Mark McCumber, Des Smyth, Russell Weir, Fuzzy Zoeller and Denis Durnian.
Watson and Kite, who were both among the early groups to tee off, remained atop a leaderboard that at one time had seven players tied for the lead.
Watson was the first of the two leaders to tee off on the Ailsa Course at the Westin Turnberry Resort. He got going at the second where he dropped a sand-wedge within 12 feet to setup birdie.
However, Watson could not maintain the early momentum. He knocked an 8-iron over the fourth green and was unable to get up-and-down to save his par.
He came back with a vengeance. He two-putted for birdie at the par-5 seventh, before running in a 20-footer for birdie at the eighth.
Watson, who out-dueled Jack Nicklaus to win the 1977 British Open Championship on this course, capped his front nine with his third straight birdie.
On the back side, the five-time British Open winner sank an eight-footer on 15 for his final birdie of the round. He was able to save par at the last despite finding a fairway bunker off the tee.
'I was very happy with the start because I didn't drive the ball well,' said Watson. 'I don't think I hit a fairway on the back side. I ended up shooting one-under par on the back side. It was not pretty off the tee for me today, but my iron play was good and I putted very well again.'
Watson and Nicklaus played together on Thursday. Earlier in the week, a plaque was dedicated on the course in honor of their duel in the 1977 Open Championship.
'The nostalgia, Jack and I talked a little bit and joked a little bit, but we're not living in the past,' said Watson. 'It was a struggle for me from the tee. It was a good day from the standpoint of understanding what my feelings were and getting the job done and getting a good score under my belt.'
Kite got off to a poor start. He dug himself an early hole as he double-bogeyed the par-4 first when his tee shot found a fairway bunker, which he blasted out of. That shot came to rest in a sand filled divot and he bladed his third shot over the green and was unable to get up-and-down to save bogey.
He managed to come right back with a birdie at the next. Kite was unable to make a 15-footer for eagle on the seventh, but settled for birdie which got him back to even-par for his round.
Kite dropped an 8-iron within eight feet to setup birdie on the 13th. He followed that up with another eight-foot birdie putt at the next.
The 1992 U.S. Open winner two-putted for birdie on the par-5 17th and joined Watson atop the leaderboard by running home a 20-foot birdie putt at the last.
'That little double-bogey on the first hole was like a slap on the face,' Kite said. 'It woke me up a little bit. I think my concentration kind of piqued from that point on. I was playing very steadily and very nice all the rest of the way around but was not quite able to capitalize on everything on the front nine. Then I made some really nice birdies on the back nine. I was quite pleased with the way I finished there.'
Bruce Summerhays heads a group of four players at 2-under-par 68. He is joined in a tie for 10th by Maurice Bembridge, Malcolm Gregson and Bill Hardwick.
Nicklaus carded an even-par 70 on Thursday. Mark Lye, making his Champions Tour debut, also posted an even-par round of 70 while the oldest player in the field, 81-year-old Jack Fleck, matched his age with an 11-over-par 81.