Asencio, 25, hit his grand slam in the first, and a two-run shot in the sixth.
The 6-foot-1, 225-pound left fielder was 2-for-3 and raised his batting average to .287 with his seventh and eighth homers. He has 38 RBIs on the season.
The Dominican Republic native signed with the Padres in 2009 under the name of Yoan Alcantara. He played in the 2013 Futures Game, on the World Team and was on the Padres' 40-man roster in 2013-14.
Asencio was named the No. 1 prospect in the Arizona Rookie League while hitting .348 with 46 RBIs and 50 runs scored in 2011. He led the low Single-A Midwest League in hitting with a .323 mark in 2012, and was a member of the Texas League postseason All-Star team last season when he hit .284 with 10 homers and 44 RBIs in 117 games with San Antonio.
Center fielder Alberth Martinez (.265) backed Asencio, going 3-for-4 with two doubles and two runs scored.
Starting RHP James Needy, a product of Santana High, improved to 2-0 with a 3.21 earned run average since moving back to 39-49 San Antonio. He allowed five runs on eight hits, and a walk with five strikeouts in seven innings.
Right-hander Michael Dimock (2.08 ERA) allowed a hit with a strikeout in two-thirds of a scoreless inning. Right-hander Tayron Guerrero allowed a hit and a walk in 1 1/3 scoreless innings to record his 11th save.
Elsewhere, El Paso infielder Cody Decker finished seventh in the Triple-A Home Run Derby in Omaha.
AROUND THE FARM:
TRIPLE-A EL PASO (45-45): The Chihuahuas are off for the Triple-A All-Star break.
HIGH SINGLE-A LAKE ELSINORE (35-52): STOCKTON 7, Storm 3 -- SS Chase Jensen (.295) was 2-for-3 with his third homer and two RBIs. CF Auston Bousfield (.288) and 3B Gabriel Quintana (.243) were both 2-for-4. Starting LHP Brad Wieck (0-2, 5.14 ERA) allowed three runs on five hits and three walks with three strikeouts in five innings.
LOW SINGLE-A FORT WAYNE (44-43): TIN CAPS 2, Great Lakes 0 -- Four pitchers combined on a six-hit shutout as Fort Wayne completed the win under a tornado warning. Starting RHP Ernesto Montas (9-5, 3.03 ERA) allowed four hits and a walk with a strikeout in five innings. RHP Seth Lucio allowed a hit with two strikeouts in two innings. RHP Yimmi Brasoban (2.22) gave up a hit with a strikeout in an inning. RHP Colby Blueberg (1.07) struck out two in a perfect inning to get his 12th save. 2B Luis Urias, 18, (.455) was 3-for-3 with a run scored. SS Ruddy Giron (.304) was 1-for-3 with a RBI. DH Edwin Moreno (.305) was 1-for-3 with a run scored. LF Franchy Cordero (.234) was 1-for-3 with a RBI. Tim Federowicz caught but was 0-for-3 in his second rehab start with the TinCaps.
SHORT-SEASON SINGLE-A TRI-CITY (14-12): DUST DEVILS 5, Eugene 4 -- C Austin Allen (.221) was 2-for-3 with a double, a RBI and a stolen base. DH Justin Pacchioli (.295) was 2-for-4 with his eighth steal and a run scored. CF Rod Boykin (.205) was 0-for-3 with two walks and two runs scored. LF Jose Carlos Urena (.298) was 1-for-2 with two walks, a steal and a run scored. Starting RHP Walker Lockett (2.53 ERA) allowed two runs on four hits and two walks with four strikeouts in six innings. LHP Jerry Keel (1-0, 1.59) allowed two unearned runs on a hit and two walks with two strikeouts in an inning to get the win. RHP Sam Holland (3.38) gave up a hit with two strikeouts in a scoreless eighth. RHP Phil Maton (2.61) struck out the side around a hit in a scoreless ninth to get his first save.
ARIZONA ROOKIE PADRES (8-11): Mariners 7, PADRES 6 -- RF Jhonatan Pena (.266) was 2-for-4 with a double, a RBI and a run scored. LF Aldemar Burgos (.251) was 1-for-3 with two walks, a RBI and a run scored. Starting RHP Adrian De Horta (9.49 ERA) allowed four runs (three earned) on five hits and two walks with four strikeouts in 3 2/3 innings. RHP Jordan Guerrero (3.68) allowed three walks with four strikeouts in 2 1/3 innings. RHP Blake Rogers (1-1, 4.91) gave up three runs (two earned) on four hits and a walk with a strikeout in 1 1/3 innings. RHP Nick Monroe (0.00) allowed a hit with three strikeouts in 1 2/3 scoreless innings.
DOMINICAN SUMMER LEAGUE PADRES (15-23): BLUE JAYS 10, Padres 2 -- The Padres made six errors leading to nine earned runs, and Padres pitchers walked 10 hitters. Right-handed starter Starlin Cordero (1-1, 7.31 ERA) allowed a run on three walks and four strikeouts in three innings. CF Carlos Taveras (.124) was 2-for-4 with a double and a RBI.