Melky Cabrera, Sandoval's teammate in San Francisco, added a two-run homer in the fourth. Rafael Furcal and Ryan Braun each tripled.
Adding to a big night for the Giants, NL starter Matt Cain tossed two sharp innings.
Chipper Jones, of the Atlanta Braves, singled as a pinch hitter on a slow grounder in the sixth inning. Perhaps happy to help Jones take a bow, Texas second baseman Ian Kinsler gave less than an all-out effort as the ball trickled into right field.
Jones has announced he will retire after this season, and had never before played at Kauffman Stadium. He tipped his batting helmet to acknowledge the crowd.
Braun also had an RBI double off Verlander during the biggest first inning since 2006, when the AL scored six times off Roger Clemens before his hometown fans in Houston.
"It's exciting for me to hit a triple with the bases loaded in the All-Star game," said Sandoval, a former Augusta GreenJacket who has only 12 triples in his career. "It's a good taste for me."
The start couldn't have tasted much better for the National League, which earned home-field advantage in the World Series for the third consecutive year.
The reward sure came in handy last season, when the Cardinals rallied to win the final two games against the Texas Rangers at Busch Stadium to capture their 11th championship. The team with home-field advantage has won three consecutive World Series, and six of the last nine.
Tony La Russa certainly enjoyed watching his guys circle the bases Tuesday night.
The former Cardinals manager retired after last year's World Series, but was asked to call the shots for the NL team one more time. He had vowed all week to manage the game to win.
Verlander was coming off two complete games in his past three starts, and had only allowed seven runs in the first inning all season. But the reigning AL MVP and Cy Young Award winner ran into trouble almost from the start, giving up a one-out single to Cabrera and Braun's RBI double.
The Detroit Tigers' ace recovered to strike out Joey Votto, but walked Carlos Beltran and Buster Posey - the latter on four pitches. Sandoval came to the plate with the bases loaded and hammered a curve off the right-field wall, driving in three runs with his first triple of 2012.
Dan Uggla, of the Braves, followed with an RBI single to deep shortstop to give the NL a 5-0 lead.
Verlander was replaced by Joe Nathan in the second inning, an embarrassing way to leave his fifth All-Star game. Verlander had allowed five earned runs in a start only once all season, and hadn't given up five runs in any inning since April 11, 2010, against the Indians.
"Obviously you don't want to go out like that," Verlander said. "That's why I don't try to throw 100 (mph) in the first inning, but this is for the fans. It usually doesn't work out too well for me."
Cain had no such problems.
The three-time All-Star worked around a single by Derek Jeter in the first inning, and then set the AL down in order in the second. Cain gave way to Gio Gonzalez in the third inning, making it a successful debut for the Giants' ace in the annual summer showcase.
Cain was hurt in 2009 and didn't enter the game last season.
"For those guys to go out there and score five runs in the first inning was definitely a little more relaxing for me," Cain said, "but I still had to stay focused."