Greinke (6-2) notched a season-high 13 strikeouts, scattered seven hits with two walks and improved to 5-0 in his last seven starts.
"Greinke is really carrying us right now," said Hunter.
Albert Pujols and Alberto Callaspo both added an RBI for the Angels, winners of four straight, who sit two games behind the Oakland Athletics for the AL's final wild card spot. The A's defeated the Texas Rangers in 10 innings earlier Tuesday.
Erasmo Ramirez (1-3) gave up five runs -- three earned -- on seven hits over six innings in the loss. The rookie right-hander struck out three and did not issue a walk.
"Erasmo made pitches tonight," said Seattle manager Eric Wedge. "He hung a pitch to Hunter, but he deserved a better fate."
Justin Smoak hit a pair of homers, including a two-run blast off Scott Downs in the seventh which cut the Mariners' deficit to 5-4.
Kevin Jepsen recorded the final out of the seventh and stranded a runner at second in the eighth before Ernesto Frieri tossed a 1-2-3 ninth to record his 21st save of the season.
Greinke's final strikeout came with the bases loaded in the fifth inning and maintained the Angels' 2-1 lead. He is the first pitcher to record 13 strikeouts in five innings since Randy Johnson in 2001.
In the bottom half, Mike Trout singled with one down and Hunter followed with a homer to left-center.
Garrett Richards struck out the side in the sixth and Aybar extended the advantage with a solo shot in the home half.
Consecutive doubles by Dustin Ackley and Franklin Gutierrez began the seventh and cut the Mariners' deficit to 5-2. Smoak's second homer of the night came later in the frame, with two down.
Trout reached to begin the game on an error by third baseman Kyle Seager, moved to second base on a single by Hunter and scored on Pujols' soft liner to right field. Callaspo added a sac fly later in the frame for a 2-0 lead.
Smoak got the Mariners on the board with a solo shot in the fourth, which landed on the top of the right-field wall and was upheld following a review.
The Angels' 20 total strikeouts marked a franchise-record for a nine-inning game. Nolan Ryan's 19 strikeouts in a 1974 contest marked the previous high ... Greinke improved to 5-1 in 12 career appearances -- 10 starts -- against the Mariners ... The Angels lead the season series, 9-5.
09/26 02:18:37 ET