Kite moved to 11 under with 18 holes to play. Second-round co-leader Peter Jacobsen shot a 2-under 69 and was tied for second with Bob Gilder (67) at 9 under.
Rain washed out play on Friday, prompting the decision to play 36 holes Sunday at Bellerive Country Club. The 7,117-yard course is the longest in the Senior Open's 25-year history. Sunday's temperature was around 90 degrees with high humidity.
Kite had seven birdies in the third round, including five of the last seven. His lone bogey came on the par-4 10th hole.
Jacobsen, playing on a surgically repaired hip that makes walking so difficult he had to withdraw from his two previous tournaments, made par on the first hole, then had a string of three birdies. He also birdied No. 14 to get to 11 under, but made bogey at Nos. 15 and 17.
Several other big names were within striking distance, including two hometown favorites.
Hale Irwin, who has a home in the St. Louis suburb Frontenac, shot a 4-under 67 to move to 8 under. Jay Haas, from Belleville, Ill., just across the Mississippi River, shot a 1-under 70 and was at 7 under.
Fuzzy Zoeller shot a 1-under 70 to move to 6 under.
Second-round co-leader Craig Stadler had 17 pars and a double bogey at the par-3 16th. He was at 5 under, along with Jose Canizares, who shot a 1-over 72.
The entire field of a Champions Tour event has never played 36 holes in one day. And unlike regular events on the Champions Tour, carts are not allowed in the five majors.
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