Byrd (6-10) scattered six hits and struck out one. His ERA is 0.86 in his past three starts.
Rumored to be targeted before last Thursday's non-waiver Trade Deadline, the right-hander tossed 7 2/3 scoreless innings Monday against Detroit, allowing just four hits. He allowed one earned in his previous start.
"I like being a part of this team and I can still get guys out," Byrd said. "I'm just going to pitch my heart out and finish with these guys or somebody's going to pick me up off waivers. I love to play baseball, compete."
His Tribe teammates are happy he stayed.
"This is a couple outings in a row where he's had command of all his pitches," said Shoppach.
Byrd attributes much of his recent success to a handful of things, including a delivery change where he keeps his hands in front instead of having them over his head, shaving his moustache, getting a new glove and receiving a suggestion from a former player.
"I got a tip on my breaking ball, keeping it down a little bit. I gave up some warning-track fly balls today, but for the most part I've kept the ball in the park the last four games, and I'll continue to see if I can make it work," he said.
Slightly laughing, Byrd refused to name his tipster.
"I don't want to get him in trouble, but, yeah, he's a broadcaster and should be in the Hall of Fame, but he's not," he said. "I'll leave it at that. I don't want to get anybody angry around here."
Former Cleveland pitcher Bert Blyleven, now a Twins television analyst, fits the bill.
Shoppach said it looks like Byrd is also standing more on top of the rubber and keeping his body a little more in control.
Byrd was only in trouble once.
Carlos Gomez and Denard Span reached on bunt singles to start the third inning, Nick Punto moved each up a base with a sacrifice bunt and Joe Mauer walked to load the bases. Justin Morneau scored Gomez with a sacrifice fly before Jason Kubel flew out to deep left-center.
Byrd calls Morneau "the least guy in the league I would like to face." This year's Home Run Derby champion teed off on a Byrd offering in the second, but it landed just foul in the upper deck.
"When he flew out there," Byrd said, "even though I gave up a run, it was a mental weight off my shoulders that he didn't hit a grand slam."
The Indians, 2-for-13 with runners in scoring position Friday, got a pair of timely hits to take a 3-1 lead in the fourth.
A bloop double by Dellucci fell between Delmon Young and Gomez to start the inning. He scored two batters later when Peralta doubled down the right-field line.
"That's really baseball," Shoppach said. "You've really got to get timely hitting. Birdy kept us in the game and we got a couple big hits."
Shoppach went down to get an offering from Kevin Slowey (7-8) two batters later. The opposite-way shot landed just over the right-field baggie for a two-run homer.
Byrd knew that he couldn't let his teammates down after that swing.
"That ball was 92 mph, down and away, on the black, not even knee high, and he shoots it out to right field," Byrd said. "When guys do that for you, you got to come through. When I walked to the field, I felt total support of my team. It fires me up. After that point, I knew this [was] our night."
Shoppach is hitting .412 with three homers and 10 RBIs in 11 games against Minnesota this year.
Asdrubal Cabrera doubled with one out in the fifth and scored on Dellucci's ninth home run of the year.
"It was good to see David step up for us," said manager Eric Wedge. "He did a great job of hustling on the bloop double and he had that big two-run homer. You talk about David's home run and you talk about Shoppach's home run, that was the difference in the game for us offensively."
Rafael Perez pitched a scoreless eighth and ninth to close out the victory.