But then Ian Kinsler homered to force extra innings, and the Rangers scored four times on the heels of the Angels' three-run 10th to prevail, 11-10. This called to mind the famous line by Houston Rockets coach Rudy Tomjanovich.
Never underestimate the heart of a champion.
While they haven't won the season's last game and reached the summit, falling tantalizingly close last October, the Rangers have appeared in two consecutive World Series. You don't do that without a whole lot of heart.
"I don't want you guys to forget it -- we're the two-time defending American League champions," Rangers manager Ron Washington was saying late Thursday night. "We came up against it the last two nights, and we fought back like champs.
"They're not going away. We're not going away. I expect it to be tight the whole way. It's going to be who plays the best down the stretch."
Unlike the Rangers, who have a family feel to their clubhouse, the Angels are a collection of athletes in search of an identity. It will be interesting to see how they respond in Chicago this weekend against the White Sox.
Here they'd been so close to shaving Texas' division lead to two games, and now it was back to five, right where it was when they alighted in the Rangers Ballpark hotbox on Monday.
This four-game series seemed more important to the pursuers at the outset, and they played like it, with passion, in seizing the first two games. But then July passed, mercifully for Texas, and the Rangers emerged from a month-long offensive slumber.
Their newly acquired starter, Ryan Dempster, had a fitful debut on Thursday, yielding eight earned runs in 4 2/3 innings. But when the Rangers' offense is rolling thunder, pitching woes can be overcome.
"We're really excited about the way we're swinging the bats," Kinsler said. "The first two games didn't go our way, but we showed a lot of life [Wednesday] night and were able to come back. Tonight was a more typical Rangers game. We scored as many runs as we needed to win the game."
C.J. Wilson, a man familiar with the Texas machinery, was the victim of their assault in this one. It began with Kinsler, the leadoff man, launching a home run and setting a distinct tone.
A total of 26 runs in two nights ought to restore confidence in your ability to produce thunder, in case any doubts had surfaced.
"We don't worry about our pitching or how many runs the other team's scoring," Elvis Andrus, the brilliant shortstop, said. "We try to win innings with our offense, attack with quality at-bats. The last few games, everybody's swinging the bats better.
"It was just a matter of time. This team never loses confidence."
Kinsler and Andrus, the catalysts, have been the most dynamic duo in the game -- until Mike Trout and Torii Hunter were aligned atop the Angels' order by manager Mike Scioscia, creating a fresh challenge.
"If you look at all good teams," Kinsler said, "the one and two guys are the ones who create havoc. Those two guys are good players."
With Trout, Hunter, Albert Pujols and Kendrys Morales all racking up big numbers, the Angels scored 40 runs and homered 13 times. No club in franchise history had rung up that many runs in a four-game series in Texas.
"That's quite a team over there," Washington said. "They don't quit. They keep coming. It's hard to go through their lineup."
Dempster surrendered more runs (eight) in 4 2/3 innings than he had (seven) in his seven starts in June and July for the Cubs. This was a rude introduction to the AL -- and the hitter's paradise that is his new home park.
"Tonight was one of those nights where if you got the ball up -- especially to right field -- it didn't come down," Washington said.
Mark Trumbo, Morales and Alberto Callaspo found the seats in right for the Angels.
Kinsler and Nelson Cruz unloaded for the Rangers, who pounded out 18 hits. Kinsler was a triple shy of a cycle.
Of the 36 runs the Rangers scored in the series, 19 came in the final nine innings.
Kinsler and Andrus, in the final two games, combined for 12 hits, seven runs and nine RBIs.
"That's what the No. 1 and No. 2 guys' job is, getting things going," Washington said. "It couldn't have come at a better time. Our backs were against the wall, and we had to fight back and show our resilience. They were the leaders."
Josh Hamilton joined the party with a two-run single against Wilson in the five-run second inning and a two-run double during the four-run seventh.
"He's our No. 3 hitter," said Washington, who'd dropped Hamilton to No. 5 with a message about showing more patience. "It looks like he's back to where he needs to be, recognizing pitches.
"Aggression can be a drawback for anyone -- not just Hamilton. It's how you use it. The times he was struggling, it was out of control with aggression. You don't want a guy getting tentative. It's something he had to work out, figure out."
Geovany Soto, the new backup catcher, singled and had a two-run double. Corner infielder Mike Olt singled in his first big league at-bat.
The Rangers appeared more relieved than excited in the afterglow of a compelling series. If have passed through the worst of times, they have to feel another memorable October is waiting for them.