The latest triumph meant significantly more to Byrd and his teammates, who regained sole possession of first place in the American League Central Division later in the evening after the Yankees put the finishing touches on a 6-1 home victory against the Tigers.
Exactly a year ago, Cleveland was 24 1/2 games off the pace of World Series-bound Detroit. Indians manager Eric Wedge prefers to dwell on the upside.
"Our guys finished strong last year," he said. "You've got to play with a lot of pride, and you've got to play with a lot of heart. Last year was a tough year, but you've still got to play the game the way it's supposed to be played."
These days, the mood among the Tribe is much better.
"It's enjoyable to come to the park every day when you've got something to play for," pitcher C.C. Sabathia said. "It starts dragging in August and September when you're not really playing for something. I'm just excited we're in the position we are now."
Interestingly, players and coaches in the Cleveland clubhouse on Saturday afternoon seemed to be more absorbed by a Little League World Series game than by the Tigers-Yankees contest being aired on adjoining televisions.
Outfielder Trot Nixon, for one, refuses to get caught up in what division rivals are doing elsewhere.
"If you're sitting here cheering for these teams and those teams, you don't have enough confidence in yourself to go out there and win the games that you need to win," he said.
In contrast, Nixon was thoroughly enjoying the showdown between the kids from Arizona and Maryland.
"Now that's baseball. That's fun to watch, it really is," he said. "I wish I was able to sit with my son and watch this stuff. It's fun."
The Indians might have had even more reason to ignore the Tigers had their bats been more productive in recent weeks. Despite a 15-18 record since the All-Star break, Cleveland has gained a game and a half on Detroit.
If lost opportunities to distance themselves from the Tigers have frustrated the Indians, they aren't saying so.
"I don't think it's frustrating. I just think that when we do put it all together at one time, we're going to be pretty dangerous," Sabathia said. "We know that we haven't been playing our best. It's still encouraging that we're still in first place."
Hot shots: Travis Hafner began the day with a .308 average, three homers and seven RBIs in eight games this season against the Rays. The designated hitter is in good company when it comes to feasting on Tampa Bay pitching. Teammates Chris Gomez (.396) and Victor Martinez (.389) are the top two hitters all-time against the Rays with at least 100 plate appearances.
Pop quiz: Grady Sizemore has collected at least 20 home runs and 20 stolen bases three years in a row. Who is the only other Cleveland player to accomplish that feat? (answer below)
This date in history: Former Indians outfielder Earl Averill was inducted into the Hall of Fame on Aug. 18, 1975. Averill was named to the American League All-Star team six years in a row from 1933-38, starting the latter three in center field. Former Pirates slugger Ralph Kiner, who closed his career with the Tribe in 1955, was also enshrined on that day in Cooperstown.
Pregame bits: Cleveland owns a .649 winning percentage (24-13) at Tropicana Field, the best of all visiting teams. ... The Tribe already has clinched its eighth season-series victory in 10 years against the Rays. ... Rafael Betancourt continues to shine out of the bullpen. The right-hander erased the only two batters he faced on Friday, lowering his ERA to 1.59. ... Barry Williams, best known for his acting role on The Brady Bunch television series, signed autographs as the Devil Rays turned the clock back to the 1970s with a disco theme.
Down on the farm: Jeremy Sowers notched his third victory in four decisions on Friday night for Triple-A Buffalo. Sowers is among several options for a promotion when Cleveland will need a fifth starter for a game at Kansas City on Aug. 25. Fellow left-handers Aaron Laffey and Cliff Lee were the leading candidates mentioned by Wedge.
And the answer is: Joe Carter turned the trick from 1986-88.
On deck: Sabathia (14-6, 3.48) will take his 7-1 career record against Tampa Bay into Sunday's series finale. Rays right-hander James Shields (9-8, 4.22) will deliver the first pitch at 1:40 p.m. ET.
Bob Bellone is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.