The left-hander made quick work of the Red Sox, using 13 pitches to preserve a 7-6 victory that clinched the best-of-five American League Division Series in Game 3 at Fenway Park on Sunday.
"You're never relaxed," said Fuentes, who had two saves in the series. "With a one-run lead, I know they're one swing away from tying it up."
In attack mode, Fuentes threw first-pitch strikes -- all takes -- to the three batters he faced. The game, and series, ended on Dustin Pedroia's soft liner to shortstop Erick Aybar.
"I think I was 3-for-3 in first-pitch strikes," Fuentes said. "In this ballpark, they've got that short porch in left and The [Pesky] Pole in right. If it's not in the back of your mind, you're crazy. To get that first out, I was thinking I was getting closer."
Fuentes prevailed on a day Red Sox closer Jonathan Papelbon watched a two-run lead disappear in the ninth inning. Papelbon actually was one strike away from extending the series to a fourth game, but Aybar had a two-out, two-strike single. The Angels went on to claim the lead on Vladimir Guerrero's two-run single.
"It was a great series," Fuentes said. "We knew coming in here that this is a tough place to win. They had the lead. Pap came in with the lead, so it was tough to get runs off of him."
Still, the job of a closer is to be ready, even when the game seemingly looks over.
So by the time Aybar was at the plate in the ninth inning, Fuentes was getting loose in the bullpen.
"I was up in the eighth, just in case we came back," he said. "I said, 'Let me get up, just in case.' You never know. Someone gets on and if you get a two-run shot, it's tied. It may not win the game, but at least you're tied. It was awesome.
"I was up. I was ready. Just the resiliency of this team. It was evident today. Guys do not give up. Vlady comes up. He had the biggest hit of the game. No matter what the score, you're ready."
Completing the sweep gave the Angels their first playoff series win against the Red Sox. Boston had eliminated them in 2004, '07 and '08.
"We've been pretty good all year," said Fuentes, who came to the Angels from the Rockies. "The AL West has been tough. Texas was tough. Seattle started sneaking in there. We're just resilient. We take a step back, and then we're marching forward.
"Coming into this series, there was a lot of talk about the past. This was my first year here. I'm about the right here, right now. We played a great series. We played fundamental baseball. We never really gave anything away."
During the season, Fuentes had 48 saves in 55 chances. For nailing down Game 3, he was presented the baseball by Aybar.
Aybar said he was hoping the final out would come his way.
"I was saying, 'Give it to me. Give it to me,'" the shortstop said. "When it was hit, I thought, 'Thank you, God.' I caught that ball."
Fuentes' perfect ninth inning capped a splendid job by the Angels' bullpen throughout the series. In the three games, the relievers allowed one run in 6 1/3 innings.
Darren Oliver appeared in all three games, and he threw 2 1/3 scoreless innings. The left-hander turned 39 on Oct. 6, two days before the series opened.
He threw one-third of an inning on Sunday and was credited with the victory.
"The guys battled back all year tremendously today," Oliver said. "We believe in each other. We won. We've got something special here. I'm just glad to be part of it. I found the fountain of youth, I guess."