Eric Byrnes hit his third home run in two days and then Conor Jackson added a three-run shot as the Arizona Diamondbacks beat the Mets 7-2 last night.

With Arizona leading 3-1, Byrnes led off the fifth inning against Mets starter Alay Soler (0-1) with his ninth homer of the season. After Chad Tracy singled and Luis Gonzalez walked, Jackson broke the game open with his sixth home run.

That was plenty of run support for Miguel Batista (5-2), who scattered nine hits with one walk and three strikeouts for the eighth complete game of his career and first since 2004. He spent last season as the closer for the Toronto Blue Jays, appearing in 71 games without a start.

Soler, the Cuban defector who was making his second major league start, allowed seven runs and eight hits in five innings.

Soler threw 95 pitches in five innings with three walks and two wild pitches.

The Diamondbacks scored two runs on one hit in the first inning.

Craig Counsell opened with a single and stole second. After Byrnes walked, the runners advanced on Tracy’s long fly ball. Gonzalez followed with a sacrifice fly, with Counsell scoring and Bynes advancing to third. When the fourth ball in a walk to Jackson was a wild pitch, Byrnes scored.

Byrnes’s home run extended his hitting streak to 13 games.

The Mets got an unearned run in the second.

Cliff Floyd and Jose Valentin opened with singles. Lastings Milledge, in his first major league at-bat, lined to shortstop. Soler bunted, and when Batista tried for the force at third,Tracy was off the base. Tracy then threw wide to first, allowing Floyd to score.

Milledge got his first major league hit, a double leading off the seventh.

In the Arizona fourth, Johnny Estrada singled with one out and scored on a triple by Orlando Hudson.

Jose Valentin hit his fourth homer in the ninth for New York.

Before the game, the Mets signed veteran catcher Mike DiFelice and outfielder Jacob Cruz to minor league contracts.

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Johnny Damon and Gary Sheffield were both out of the New York Yankees starting lineup Tuesday night against the Detroit Tigers due to injuries.

Damon asked for a day off because of continued problems with his right foot, while Sheffield was scratched from the lineup just before game time due to soreness in his left wrist.

Damon broke a bone in his right big toe when he crashed into the wall on April 18 in Toronto, and aggravated the injury earlier this month.

“I think we’re going to have to do this from time to time,” Damon said. “We played a day game [Monday] and we’ve got a night game [today), so this will almost feel like two days off.”

Sheffield injured his wrist in a collision with Toronto’s Shea Hillenbrand on April 29.

He missed the next three games, pinch hit in another and made one more start before going on the disabled list. Sheffield was activated last week when the Yankees played the Red Sox in Boston.

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DODGERS ACTIVATE GAGNE The Los Angeles Dodgers activated closer Eric Gagne yesterday but announced he began serving a two-game suspension and will not join the team until Thursday in Los Angeles.

Gagne completed his second minor league rehabilitation stint with Triple-A Las Vegas Monday, recording a save in an 8-6 victory.

“My arm felt great,” Gagne said after a pitching a scoreless inning for Las Vegas. “I feel confident. I’ll be ready for Thursday.”