Cruz's single off Brian Sweeney, Italy's third pitcher used in the seventh, scored Robinson Cano with the go-ahead run, prompting the entire Dominican bench to leap out of the dugout.
The hard-fought, emotional win improved the Dominican Republic to 4-0 in the Classic and put it in prime position in the double-elimination second round. The Dominicans will face Team USA -- 7-1 winners Tuesday against Puerto Rico -- on Thursday night at 7 ET on MLB Network and ESPN Deportes.
"Whenever you go against a team between the two white lines, you don't know what you're going to get," Dominican manager Tony Pena said. "This has to be the toughest game that we have played in the WBC."
A majority of the 14,482 at Marlins Park were rooting for the Dominican Republic. But until the seventh, Italian starter Tiago Da Silva mostly silenced the star-studded squad.
"What I'm asking from my guys is to leave it all out on the field," Italian manager Marco Mazzieri said. "We did that today. Actually, I was saying, 'Let's look at scoreboard at the end.' Unluckily today, the scoreboard was not on our side."
Cano and Jose Reyes each hit solo homers off Da Silva, who gave up two runs in 5 1/3 innings.
"Our team never lowered our heads," said Reyes, who was 2-for-5 with two runs scored.
Cano made an impact in the middle of the order, going 3-for-4 with a double, homer and two runs scored.
"It's difficult to begin 4-0," the Yankees' All-Star second baseman said. "But the great energy on our team -- we never gave up."
The Dominicans out-hit Italy, 10-4, and they were able to break through with their three-run seventh inning.
Reyes started the rally with a one-out single off Pat Venditte. Erick Aybar followed with a single, and Cano was credited with a single on a soft fly ball to short left field. In spacious Marlins Park, left fielder Michael Costanzo was playing deep, and he was unable to make up ground. Shortstop Anthony Granato raced back and got his glove on the ball, but fell in, loading the bases.
Reliever Luca Panerati replaced Venditte and walked Edwin Encarnacion on four pitches, forcing in a run. In came Sweeney, who yielded a Hanley Ramirez sacrifice fly to center, pulling the Dominican Republic even at 4.
The intensity of the game was evident from the first inning. The underdog Italian team repeatedly gave all-out hustle on even the most routine plays. It almost led to an incident with Cano at second base. Three different innings ended with Cano making force outs at second. All three times, Italy's baserunners slid hard into the bag, clipping Cano's leg.
Cano became fed up after Nick Punto made contact on a slide in the seventh.
"Yeah, I was upset, because it was the third time in the game," Cano said. "I don't care if you slide in on a double play, but when it's a force out at second base, the last thing you want is to get hurt like that. They're passing the base."
Italian hitting coach Mike Piazza responded: "You never take anything for granted in this game. There is a difference between hard baseball and dirty baseball. If he bobbles the ball, and we're not running hard, and we're out, that's not good baseball. You have to put your effort into being safe."
Grinding out at-bats helped Italy take a four-run lead in the first inning, powered by Chris Colabello's three-run homer off Dominican starter Edinson Volquez.
Volquez regrouped and threw 4 1/3 innings, striking out three. But he was hurt by four walks.
"He wanted to do so good, that he found himself in trouble," Pena said. "After the first inning, he did a great job settling down and keeping us in the ballgame."
The Dominican Republic, winner of Pool C, entered Round 2 after a dominating performance in the first round in Puerto Rico. In its first three games, it scored 19 runs on 34 hits.
The pitching was equally impressive, combining for a 2.67 ERA.
But what transpired in Puerto Rico didn't carry over to Miami, at least it didn't in the first inning.
Volquez walked the first three batters he faced -- Punto, Chris Denorfia and Anthony Rizzo. Of his first 13 pitches, 12 were balls.
Alex Liddi's sacrifice fly to right put Italy on the board, and designated hitter Colabello made it a big inning with his three-run homer.
The 29-year-old Colabello is in the Twins' Minor League system, and he's enjoying a memorable Classic. He had a four-RBI game, including a three-run homer, on Friday in Italy's 14-4 win over Canada in Phoenix.
But after Colabello's long ball, Volquez didn't allow another hit until the fifth inning.
From that point, the Dominican Republic chipped back on Reyes' homer in the third inning and Cano's blast in the sixth, setting the stage for the game-turning seventh.
"They kept talking in the dugout, 'Hold it right there, we're going to come back and win the game,'" Pena said.