The Halos racked up five runs in the first inning, with Mark Trumbo adding to Hamilton's three-run shot, and Albert Pujols, Hamilton and Brendan Harris all went deep in a six-run fifth.
Even with defeats for American League West Division pace-setters the Oakland Athletics and Texas Rangers, though, the Angels still remained a distant third.
They are nine games behind the As, who went down 5-0 to the Pittsburgh Pirates, and 8.5 adrift of the Rangers, beaten 6-1 by the Baltimore Orioles.
Nolan Reimold's three-run homer helped Baltimore to a win which keeps them in contention in a competitive AL East.
Leaders the Boston Red Sox hammered the Seattle Mariners 11-4 with a landmark for David Ortiz.
Ortiz's second-inning double was an MLB-record 1,689th hit as a designated hitter, and he celebrated with a two-run homer in the third and later scored Shane Victorino on a sacrifice fly.
The second-placed Tampa Bay Rays needed 13 innings to edge out the Minnesota Twins 4-3, Ben Zobrist's walk-off single scoring Yunel Escobar.
The New York Yankees remain within six games of the Sox after beating the Kansas City Royals 8-1. Lyle Overbay hit a grand slam and Robinson Cano a three-run homer.
The Detroit Tigers extended their lead of the AL Central to 3.5 games with an 8-5 win over the Chicago White Sox. Prince Fielder had three RBI including a two-run homer in the first inning.
The second-placed Cleveland Indians lost 5-4 to the Toronto Blue Jays after a 3-2 ninth inning. Munenori Kawasaki hit the decisive shot, scoring Colby Rasmus, JP Arencibia and Emilio Bonifacio.
In the meeting of the National League West's top two, Hanley Ramirez and AJ Ellis hit back-to-back home runs off Josh Collmenter to start the 14th inning as the Los Angeles Dodgers outlasted the Arizona Diamondbacks to claim a 7-5 win.
Kenley Jansen picked up the win with two innings of relief, the Dodgers' bullpen throwing a two-hit shutout over the final nine innings after starter Hyun-Jin Ryu allowed five runs in five innings.
The win completed a three-game sweep and left the Dodgers one and a half games behind the first-placed Diamondbacks.
The Colorado Rockies beat the San Diego Padres 5-4 while the San Francisco Giants lost 7-2 to the New York Mets.
In the Central Division, the St Louis Cardinals maintained their two-game lead over the Pirates as Matt Carpenter's two-run homer earned them a 5-4 win over the Houston Astros.
The third-placed Cincinnati Reds remain five games back after a 6-2 win over the Milwaukee Brewers, Mike Leake pitching into the ninth for the win.
NL East leaders the Atlanta Braves suffered a surprise 6-2 loss to the division's basement boys the Miami Marlins, Giancarlo Stanton's two-run double sparking a four-run first inning to deny Atlanta a series sweep.
The Washington Nationals closed the gap with a 5-1 win over the Philadelphia Phillies in the meeting of the second and third placed teams.
The fifth and sixth innings both began with back-to-back Washington homers, Ryan Zimmerman and Jayson Werth matching the feat of Anthony Rendon and Wilson Ramos.