Watson, who has two Top 10 finishes on the Champions Tour this year, matched his best round of 2009.
"It's nice to have a good round and have some fun," the 58-year-old Watson said. "All in all, I was very happy."
With overcast skies, a light drizzle and whipping winds, Watson said the course at Prestonwood Country Club played long.
"There were some difficult shots if you didn't hit in the fairway," he said. "And the wind was whipping pretty good today."
Cochran, who finished tied for second last week at the Greater Hickory Classic, said he got several lucky breaks in his round.
"I putted well, but I got a little help," said Cochran, who chipped in from a greenside bunker for birdie on No. 10, a 428-yard par 4. "No. 10 was my big break of the day. I drove it good, but I hit a terrible 5-iron and hit it into the bunker on the right."
Cochran's bunker shot landed past the pin and spun back into the hole.
A Champions Tour rookie this year, the 50-year-old Cochran has had to rely on sponsor exemptions and is trying to remain in the Top 30 on the money list to qualify for the Charles Schwab Cup Championship in October in Sonoma, Calif.
At the end of June, Cochran was in 70th place in season earnings. Since then, he has moved up to No. 28, thanks in part to his Top 5 finishes at the U.S. Senior Open in August and last week at the Greater Hickory Classic.
Cochran called last week's tournament a breakthrough for him because he stopped worrying about Top 10 finishes, money lists and exemptions.
"I said that if I'm going to have any kind of success, I'm just going to have to go at the hole," he said. "Anything that takes away from your aggressiveness hurts you."
Fred Funk and Loren Roberts, who are first and second in the Charles Schwab Cup points race, both shot 70s to finish the first round at 2-under, four shots off the pace. Funk leads Roberts by 57 points for the Schwab Cup.
Defending champion Eduardo Romero carded a 3-over 75 and is tied for 62nd.
The SAS Championship was Leonard Thompson's 1,000th tournament on the PGA and Champions tours, dating back to the 1971 U.S. Open. Thompson joined nine other players to play in at least 1,000 events.
Thompson, 62, a North Carolina native and Wake Forest graduate, said 1,000 tournaments isn't something you set out to do.
"But once I knew I was going to do it, I tried to arrange to do it here," said Thompson, who was greeted with a cake after his round of 74.