Support has been nearly non-existent for Darvish so far.
The Rangers ace will try to end his woes against the Athletics as these AL West rivals open their season series by beginning a three-game set Monday night in Oakland.
Darvish (1-0, 0.82 ERA) beat Oakland on May 16, 2012, but has posted a 4.95 ERA in losing his next six meetings. Texas has given him six runs of total support in that slide.
The Rangers (11-8) haven't scored for Darvish in his last two outings since he pitched seven innings to earn a 3-0 victory at Tampa Bay on April 6. The right-hander opened the season with 16 scoreless innings, and yielded his first two runs Wednesday over seven innings in a 3-2 home win over Seattle.
Darvish will be wary of Brandon Moss, who is 5 for 15 with three homers against him as one of only four players to have taken Darvish deep at least that many times.
Whether the Rangers can provide him some offense will depend on how they fare against Dan Straily (1-1, 5.40), who is 3-0 with a 4.03 ERA in his last four starts against them.
No hitter in baseball has fared worse against Straily than Elvis Andrus, who is 0 for 14 with five strikeouts.
Straily gave up six runs over 3 2-3 innings Tuesday in a 10-9, 11-inning victory over the Los Angeles Angels. The right-hander gave up more than three runs for the first time in nine starts.
Oakland slugger Yoenis Cespedes is 3 for 14 with a homer and nine strikeouts against Darvish. He homered a team-high five times against the Rangers last season as the A's took 10 of 19 meetings.
Cespedes left Sunday's 4-1 win over Houston in the seventh inning with a bruised right heel and was replaced by Craig Gentry.
Oakland (13-5) is seeking its third four-game win streak of the season after Josh Donaldson homered and drove in three runs Sunday. Donaldson is hitting .345 with 12 RBIs over his last 12 games.
Kouzmanoff, filling in for an injured Adrian Beltre, will face Oakland for the first time since his time with the A's from 2010-11. Kouzmanoff was traded to Colorado on Aug. 23, 2011, before spending the last two seasons in the minors for two different clubs.
Gentry could play his first game against the club with which he spent his first five seasons, although he has started just four times. He was traded to Oakland in the offseason.
"I want to beat every team, but coming from there, it kind of gives you a little more incentive," Gentry told the Athletics' official website.
Oakland owns an AL-best 2.48 ERA but has committed two errors in four straight games, and has made at least one in nine in a row.
''I don't like it,'' manager Bob Melvin said. ''You can't continually play defense like this and get away with it.''