Cochran and Clearwater had rounds of 5-under 66 at the Oak Hills Country Club, which for 21 years hosted the San Antonio stop on the regular PGA Tour.
The top 30 money winners on the Champions Tour are eligible to play next week at the Charles Schwab Cup Championship. Cochran is relatively safe to make the field for that event since he currently stands at 23rd on the money list.
Clearwater, who is 110th in earnings, would not make the Schwab Cup tournament even if he won this week.
Two-time defending champion John Cook, who won last week's Administaff Small Business Classic, shot a 68 and in a large group tied for seventh place.
Notable deaths of 2014 [PHOTOS]