Miller threw 6 1/3 impressive innings and the Red Sox took the final three matchups in a four-game series between AL division leaders.
Gonzalez hit a solo shot in the first inning and a two-run drive in the third off Alexi Ogando (12-6), giving him homers on three consecutive swings — including one in the eighth inning of Boston's 13-2 victory Wednesday night.
Gonzalez, who had his 13th career multihomer game, had gone 84 at-bats without a long ball before homering in the first inning of Tuesday night's 11-5 win.
David Ortiz and Jarrod Saltalamacchia also connected for the Red Sox, who have won six of eight and remain one game ahead of New York in the AL East. The Yankees pounded Oakland 22-9 earlier Thursday.
Miller (6-1) struck out six and walked two in his 10th start of the season. The lanky left-hander, who has also pitched in relief twice this season, got the assignment because manager Terry Francona pushed right-hander Tim Wakefield back a day, giving the knuckleballer his sixth shot at his 200th victory at home Friday night against Oakland.
The Rangers, who have dropped five of six, held a seven-game lead in the AL West over the Los Angeles Angels on Aug. 17. That margin has shrunk to two games entering Friday night's opener of a three-games series between the teams in Texas.
The streaking Angels, who have won six straight, were idle Thursday.
Ogando allowed a career-high four homers — the same number he yielded in his previous 12 starts — among his six runs and six hits in four innings as he failed to join C.J. Wilson as the Rangers' second 13-game winner.
Texas was a 4-0 winner in the opener of the series, but Boston took the final three games by a total score of 30-7.
With two outs and nobody on in the first, Gonzalez lofted Ogando's fastball onto the grass hill beyond the center-field wall.
Ortiz led off the second with a drive into the right-field seats for his 25th homer to give Boston a 2-0 pad. Ortiz had missed nine games because of bursitis in his right heel before returning to the lineup Wednesday night when he went 2-for-5 and scored twice.
Ortiz has his eighth 25-homer season for Boston, second in club history behind Ted Williams' 14. Ortiz started the night tied with Jim Rice at seven.
With Jed Lowrie on first after a walk in the third, Gonzalez pounded another Ogando fastball 448 feet into the Red Sox bullpen in left-center for his 23rd homer and a 4-0 edge.
Carl Crawford opened the fourth with a single and Saltalamacchia, traded by the Rangers to the Red Sox in July 2010, launched a two-run shot for his 13th of the season to stretch the lead to 6-0.
Notes
The Red Sox have switched Sunday's scheduled finale of a three-game home series against Oakland to Saturday night as part of a day-night doubleheader because of the threat of bad weather due to Hurricane Irene. Oakland isn't scheduled to play west of the Mississippi after completing the Boston series, so making up a rainout would be difficult for the A's. … Boston OF J.D. Drew (left shoulder) is expected to DH in a minor league rehab assignment sometime this weekend. The team he's assigned to will depend on the weather in New England. … Texas LHP Derek Holland (11-5) gets the start Friday night against Dan Haren (13-6) of the Angels. … Four hours before the game began, Rangers 3B Adrian Beltre slowly ran the bases as he continued his rehab from a strained left hamstring that landed him on the 15-day DL on July 23. Manager Ron Washington said there's no schedule for the All-Star to begin a minor league rehab assignment.