Morneau homered and Blackburn pitched seven solid innings in the Minnesota Twins' 5-1 victory on Friday night.
It was the first time in 17 games this season that the Twins didn't trail.
"I hate it," Minnesota manager Ron Gardenhire said with a laugh. "It was more fun the other way. We love being behind."
Morneau hit Fausto Carmona's first pitch of the fourth into the seats in right to give the Twins a 2-1 lead, and also drove in a run with a fielder's choice in the seventh. Morneau batted .351 (13-for-37) with a homer, five doubles and 10 RBIs in nine games at Progressive Field last season.
"I missed the pitch with Morneau," Carmona said. "I missed inside a little."
Three nights after drawing 11,408 fans -- the lowest total in the history of the ballpark that opened in 1994 -- Friday's game attracted 20,215. Many of them showed up for a postgame fireworks show.
Approximately 17,000 fans jammed nearby Quicken Loans Arena to watch the Cavaliers' NBA playoff game in Detroit on the arena's television screens. The biggest cheer of the night at the ballpark came when the Cavaliers' 79-68 win was shown in the scoreboard.
Blackburn (1-1), winless in his first three starts, allowed one run and six hits. The right-hander was 3-0 and allowed four earned runs over 27 2/3 innings in four starts against Cleveland last season.
"I'm not sure," Blackburn said when asked why he has been so successful against the Indians. "They're a fastball-hitting team. They're pretty aggressive. I assume that's what it was."
Carmona (1-3) allowed five runs in six-plus innings.
The win snapped a four-game road losing streak for the Twins, who were outscored 31-5 in that stretch.
Blackburn got some help from pitching coach Rick Anderson after the Indians scored in the third inning. Asdrubal Cabrera started the rally with a one-out double and scored on Grady Sizemore's single. After Mark DeRosa followed with a single, Anderson went to the mound and told Blackburn to start using his breaking pitches to keep the hitters off balance.
"His sinker was pretty good tonight, better than in the past," Cleveland's Ryan Garko said. "He's always had a good cutter and breaking ball, but his sinker was better on both sides of the plate."
Minnesota added a run following Morneau's homer, thanks to third baseman DeRosa's throwing error. DeRosa made a diving stop of Delmon Young's hard-hit grounder, but his throw to second for a force play sailed into right field. Jose Morales' single put the Twins up 3-1.
Minnesota added two in the seventh. Carmona was pulled after allowing singles to the first two batters. Following Morneau's RBI fielder's choice, Joe Crede knocked in a run with an infield hit.
Twins closer Joe Nathan, who hadn't pitched since Sunday, threw a scoreless ninth.
Twins C Joe Mauer (back) began a rehab assignment at Class A Fort Myers. He was 2-for-4 with two RBIs and played seven innings. ... Twins minor league first baseman Hank Sanchez was suspended 50 games after testing positive for a drug of abuse. Sanchez was batting .231 with two RBIs in four games for Class A Beloit. Sanchez was the 11th player suspended this year for violating baseball's minor league drug program. ... RHP Adam Miller, the Indians' top pitching prospect, likely will undergo career-threatening surgery on his right middle finger next week. He had surgery on the finger last May, but still felt pain while throwing. ... LHP Scott Lewis (sore elbow) has begun a throwing program at the Indians' complex in Goodyear, Ariz.