Utley hit a three-run homer and Victorino and Dobbs each had two-run shots during a 10-run first, leading the Phillies to a 22-1 victory over the Reds on Monday night.
The previous worst defeat for the Reds, baseball's first professional franchise, was 26-6 on July 26, 1892. That also was against the Phillies.
"We got slaughtered as they used to say," Reds manager Dusty Baker said.
Hamels (5-5) was the beneficiary of the offensive outburst. The struggling ace allowed one run and three hits in seven innings to earn his first win since shutting out the Los Angeles Dodgers on June 4.
"I was just jumping for joy," Hamels said about the run support. "When you put that many runs up, it makes it uncomfortable for the other team."
The Phillies tied a club record for most runs in the first inning. They scored 10 three other times, most recently on June 2, 2002, against the Montreal Expos.
It was the most runs by Philadelphia since a 26-7 win over the New York Mets at the old Veterans Stadium on June 11, 1985. The 22 runs were the most in the six-year history of Citizens Bank Park.
Reds starter Johnny Cueto (8-5) retired just two batters, allowing nine runs and five hits. It was the shortest outing in the right-hander's two-year career. Cueto had never allowed more than six earned runs in a game, and his ERA rose from 2.69 to 3.45.
Werth connected off Paul Janish in the eighth. Victorino, a candidate for the final spot on the NL's All-Star roster, helped his case with four hits, four RBIs and a career-high five runs. Dobbs had four hits, Utley drove in four and every starter had a hit.
"It was one of those nights where everything we hit was falling and we hit some hard," manager Charlie Manuel said.
The NL East-leading Phillies have won four straight games after losing 14 of 18. They hadn't scored more than 15 runs since a 20-2 victory at St. Louis last June 13. After that game, the Phillies went 3-11 and scored a total of 38 runs.
Rollins led off Philadelphia's first with a walk and Victorino followed with a liner into the right-field seats. Cueto struck out Utley and Ryan Howard lined out, but the next eight batters reached.
Werth singled and Dobbs drove one out to right. Cueto then hit Pedro Feliz and walked Carlos Ruiz before Hamels ripped a double down the right-field line to score both runners. Rollins doubled to left-center, scoring Hamels for a 7-0 lead. Cueto left after he walked Victorino. Danny Herrera came in to face Utley, who hit a towering drive to right-center to make it 10-0.
Hamels, the MVP of the World Series and NLCS last year, has had a frustrating season. The left-hander was nagged by injuries early and hasn't pitched well consistently. He got chased in the fifth inning in each of his last two starts.
The Phillies are scouting free-agent pitcher Pedro Martinez in the Dominican Republic. The three-time AL Cy Young Award winner was 5-6 with a 5.61 ERA for the Mets last season. ... Phillies LF Raul Ibanez went 0 for 2 with a strikeout, walk and scored a run in his first rehab start at Double-A Reading. Ibanez played the first five innings in the field and didn't have any chances. He's expected to get a few more rehab starts to test his injured groin. Ibanez, who was voted to his first All-Star Game, is batting .312 with 22 homers and 59 RBIs. ... The Reds allowed a season high for runs. ... The Phillies had a season-high 21 hits. ... Janish allowed six runs in one inning in his second appearance on the mound. He gave up five runs in one inning during a 15-3 loss to Milwaukee on May 6. ... The previous high at Citizens Bank Park was 20 runs by the Phillies last May 26 against Colorado.