The pair leads Bobby Walzel, who shot 6-under-par 66. Hugh Baiocchi, Dick Lotz, Walter Hall and Mike McCullough are all tied for fourth at 4-under.
Both Dougherty and Eastwood started the first round with a birdie at the par-4 first. Dougherty, 53, went on to record an eagle at the par-5 10th to go along with six birdies and one bogey. Eastwood, 55, recorded seven birdies and no bogeys.
Walzel is coming off a tie for second at last week's Verizon Classic. Friday, the 51-year-old rookie tied a career best on the Senior circuit by posting a 66. His round included eight birdies and a double bogey at the par-4 11th. Walzel encompassed the double with five birdies over his first eight holes and three birdies over his final four.
Defending champion Hubert Green is 15 shots off the 18-hole lead after carding an 8-over-par 80.
Click here for Full-Field scores from the Mexico Senior Classic!