It only figures to get worse for them in 2013.
The Rays look to take advantage of baseball's worst team in the first of four straight against Miami on Monday.
These in-state foes play two games at Tropicana Field before a pair in Miami on Wednesday and Thursday.
The Marlins (13-37) are off to the worst start in franchise history and the poorest in the majors since the 2006 Kansas City Royals had the same record. No NL team has started this slowly since the 1987 San Diego Padres were 11-39.
They averaged 3.0 runs in losing nine of 12 over the last two years to Tampa Bay (25-24) in the 'Citrus Series.'
Those Marlins teams were poor offensively, with the 2011 club averaging 3.9 runs and last year's 3.8. That's a far cry from what Miami is producing this year - 2.6 runs per game.
The last teams to average fewer than three runs were the 1972 Texas Rangers (2.99) and 1972 California Angels (2.93).
Miami has been particularly bad offensively while losing 15 of 18, batting .207 with just six homers and averaging 1.9 runs.
"You put up eight runs against the Yankees, definitely something good, but the `W' is all that matters," Rodriguez said.
Evan Longoria had a quiet weekend series with three hits in 13 at-bats, and he's gone five straight games without an RBI. He has never enjoyed much success against the Marlins, hitting .227 in 24 games.
Longoria and the Rays will get their first look at Miami starter Jose Fernandez (2-2, 3.31), a right-hander who is limiting hitters to a .215 average.
Fernandez is 2-0 with a 2.48 ERA over his last five starts, yielding one run over five innings Tuesday in a 7-3 home defeat to Philadelphia.
"Every time I can go out there and give the team a chance to win and a chance to stay in the ballgame, I'm happy," Fernandez said.
Tampa Bay will also start a rookie right-hander in Jake Odorizzi (0-0, 5.40), who gave up three runs over five innings last Monday in his club debut in a 7-5 loss at Toronto.
Odorizzi, whose previous big-league experience consists of two starts for Kansas City in 2012, is taking the place in the rotation of the injured David Price.
One young player who may have some extra incentive for the Marlins is Derek Dietrich, drafted in the second round by the Rays in 2010. Dietrich was traded to Miami on Dec. 4, 2012, in a deal that brought Yunel Escobar - acquired by the Marlins a month earlier in the Josh Johnson deal - to Tampa Bay.
Dietrich, hitting .232 overall but with two homers in his last three games, was promoted to the major leagues on May 8 for Miami.
The Marlins have dropped five straight after scoring seven runs over the weekend in a three-game set against the White Sox.