Alfonso Soriano and Herbert Perry assured the victory as they each drove in two runs.
The 39-year-old Rogers (2-0) allowed just five hits while walking two and striking out one. The lefthander, who is in his third stint with the Rangers, taught a lesson to Oakland starter Rich Harden, a 23-year-old who struggled in his first start of the season.
Called up from the minors before the game, Harden (0-1) was tagged for six runs and 11 hits in four-plus innings.
Perry and Kevin Mench had RBI singles in the fourth before the Rangers broke open the game with four runs in the fifth.
Texas loaded the bases on a double by Rod Barajas, a single by Michael Young and a walk to Hank Blalock. Soriano delivered a two-run single and Brad Fullmer drove in another run with a single, finishing Harden.
Chris Hammond relieved and allowed a sacrifice fly to Perry that made it 6-1.