NEW YORK -- Ryan Dempster is too busy watching "Swamp People" to see the stories about him being possible trade bait. He's pitching too well, though, to know that he might be in another uniform by the end of the month.

Dempster extended his scoreless innings streak to 27 in his first start in three weeks, Starlin Castro hit a three-run homer, and the Chicago Cubs beat the New York Mets 7-0 on Sunday.

"I don't really notice a lot of the rumors," Dempster said. "I just handle what I can handle and that's going out there and pitching and doing my job. Wherever the cards fall they fall."

Dempster (4-3) was activated from the disabled list, then pitched five innings of four-hit ball in his first outing since June 15, when he experienced tightness in a back muscle. His lengthy string of zeros is the Cubs' most for a starter since Ken Holtzman went 27 innings in 1971.

The Cubs made it as comfortable as possible for Dempster, scoring four runs before he even threw a pitch.

Alfonso Soriano had an RBI single, Jeff Baker a run-scoring double with a jam shot to the opposite field, and Geovany Soto drove in two runs with a single against Jonathon Niese.

Niese (7-4) had only given up four or more runs in a game five times -- 16 starts -- this season entering Sunday.

"They came out swinging," Mets manager Terry Collins said. "He was trying to get ahead (and) they were hammering the first pitch."

The Cubs finished the first half in the midst of a modest surge, winning nine of 13 to improve to a disappointing 33-52 in Theo Epstein's first year in charge. It's their worst record before the break since 2006, when they were 34-54.

"The team has been a little up and down but everybody hustles right now," Castro said. "Let's see in the second half everybody pull a little bit together and win more games."

The Mets had a chance to move a season high-tying eight games above .500 but continued a recent trend of trading wins and losses. They enter the All-Star break 46-40, their best first half since 2010, when they were 48-40. New York finished a homestand against two last-place teams, Philadelphia and Chicago, 3-3.

Not that the Mets didn't have their chances Sunday. They put runners in scoring position in each of the first three innings and also in the sixth but came up empty.

Dempster put his streak in jeopardy by allowing a one-out triple to Scott Hairston in the second, but he got Jordany Valdespin to line out to second and Josh Thole to ground out to shortstop. Niese and Ruben Tejada opened the third with singles, but the Nos. 2-3-4 hitters couldn't capitalize.

After Tejada's hit, Dempster retired nine in a row before being lifted.

"He was way more efficient than we thought," Cubs manager Dale Sveum said. "Everything went well. He feels great."