Marlon Byrd added an RBI single and Kosuke Fukudome was 3 for 3 with an RBI double, a walk and two runs scored for the Cubs.
Marshall, battling for a spot in the rotation, scattered three hits and gave up an unearned run with a walk and five strikeouts.
"I'm not saying I'm the perfect candidate for it but I love to start. I want to start," said Marshall.
Cubs manager Lou Piniella said earlier this week he'll announce his rotation on Friday. Marshall, who has allowed three runs -- two earned -- on seven hits over 11 innings this spring, remains in the mix along with fellow lefty Tom Gorzellany.
"My attitude is always to keep a positive attitude whatever role I'm in and help the team win some games," Marshall said. "We'll see what happens."
Texas starter Brandon McCarthy allowed four runs on four hits in a 45-pitch first inning. The right-hander lasted 3 1-3 innings, giving up eight hits with four walks and a strikeout.
"I'm definitely not happy with the results," said McCarthy, who also opened with a 40-pitch first inning in his last start. "It comes down to outs and keeping runs off the board and in that area I was lacking."
Rangers manager Ron Washington said it was unlikely McCarthy, whose ERA ballooned to 8.03, would move to the bullpen.
"He's a guy who's got routines," he said. "I'm not going to say absolutely no but it's not something we've talked about."
The Cubs added six runs in the sixth off Rangers reliever Luis Mendoza and two more in the seventh. Chicago finished with 17 hits.
"We had 12 ground balls and there wasn't anybody there to catch them," Washington said.