Urbina, who helped the Florida Marlins win the World Series in 2003, is 1-3 with nine saves and a 2.63 ERA in 25 games. He hasn't allowed a run in his last 10 innings.
Polanco, who platooned with Utley and started at three other positions, is batting .316 with three homers and 20 RBI. Martinez is hitting .268 in 19 games, including 15 starts.
"The price was high, but to be able to get a proven bullpen arm who has pitched at a championship level, it was too good to pass up," Phillies general manager Ed Wade said, adding that Tigers president Dave Dombrowski told him he was close to moving Urbina to another team in the NL East.
Urbina, a two-time All-Star, is 40-46 with 236 saves and a 3.39 ERA in 11 seasons with Montreal, Boston, Texas, Florida and Detroit. The 31-year-old right-hander will pitch in a setup role with the Phillies and be used as a closer when Billy Wagner needs a rest.
Urbina provides depth in a bullpen that also features Ryan Madson, who has pitched well setting up Wagner.
The Phillies expect Urbina and Martinez to be available for Thursday night's game against Texas. Polanco will join Detroit in Colorado on Friday.
"He'll be a big part of our bullpen," Phillies manager Charlie Manuel said. "He'll go right to the back part. This helps because [Rheal] Cormier, Madson and Wagner have been overworked."
A versatile infielder, Polanco was a full-time starter in his first 2½ years with the Phillies after coming to Philadelphia in a trade that sent third baseman Scott Rolen to St. Louis in July 2002. Polanco had his best season last year, hitting .298 with a career-high 17 homers and 55 RBI in 126 games.
But the Phillies planned to make Utley their regular starter going into this season and were surprised when Polanco accepted arbitration and signed a $4.6 million, one-year contract in December.
So Manuel used Polanco at second base against left-handed pitchers and also gave him some starts at third base, shortstop and left field.
"It's sad to be leaving good friends, but I'm happy because I'm going to play more," said Polanco, who is expected to be Detroit's regular second baseman. "I just wanted to play. I wanted to stay here my whole life."
Utley, a fan favorite and former first-round pick, was hitting .315 with nine homers and 29 RBI in 149 at-bats.