Lawrie's third career slam made it 5-0 in the first off Wandy Rodriguez (4-3), who had never before faced the A's in his 11-year major league career. Oakland led 8-0 after two innings.
A's rookie center fielder Billy Burns led off each of the first two innings with doubles, and scored both times on hits by Stephen Vogt. Burns also singled in the third and has a 14-game hitting streak, with hits in 26 of his last 27 games.
Kendall Graveman (4-4) allowed two runs over seven innings. It was his fourth consecutive game to pitch at least seven innings while allowing two runs or less, but the right-hander had been 0-2 in the previous three.
Lawrie's slam went an estimated 422 feet, landing in the A's bullpen in left-center field. Phegley's fifth homer of the season was a two-run shot in the second to make it 8-0.
Carlos Corporan had a two-run double for the Rangers, who have lost four in a row for the first time since April 27-May 1.
Texas had won its last six games started by Rodriguez, who had allowed three runs or less in each of those games. The lefty gave up 11 hits and eight runs while throwing 94 pitches in four innings against Oakland.
Second base umpire Dale Scott sustained a bruised left thigh and was out of the game for 2 1-2 innings after being struck by Lawrie's liner with two outs in the fourth inning.
A Rangers trainer immediately went to check on Scott. The crew chief walked gingerly off the field after briefly conferring with the trainer. Scott grimaced in pain, but never left his feet.
The umpires worked as a three-man crew until Scott returned to the field for the start of the seventh inning.
Earlier this month at Fenway Park in Boston, a Massachusetts woman was struck on the head by Lawrie's broken bat and hospitalized for a week.
Athletics: Vogt returned to the lineup, at first base instead of catching for his first game since a cortisone injection in his left elbow Sunday. It was his 10th start at first, but manager Bob Melvin expects Vogt to make his 48th start at catcher in the series finale Thursday.
Rangers: LHP Matt Harrison pitched six innings for Double-A Frisco, his fifth rehab start in his recovery from spinal fusion surgery last year. ... Slugger Josh Hamilton (strained left hamstring) played in that same game, going 1-for-3 with a double, a walk and a hard liner for an out. Hamilton will join Triple-A Round Rock on Thursday.
Athletics: Sonny Gray (8-3), whose 1.95 ERA is best in the AL, has allowed only one run over 31 1-3 innings in his four previous starts at Texas. He threw two shutouts there last year.
Rangers: The Rangers try to avoid a series sweep and their first five-game losing streak this season. Scheduled starter Colby Lewis is 3-0 with a 2.79 ERA his last four starts.