Cain, closer Armando Benitez and the Giants had to settle for a combined two-hitter and a 2-1 win over the Angels.
The victory snapped a three-game slide for the Giants and evened San Francisco's record at 35-35.
Cain (6-5) lost the shutout long before he lost the no-hitter. Figgins led off the game with a walk, stole second and kept on going all the way to home plate when catcher Eliezer Alfonzo's throw skipped into left field.
"When I threw that ball and they scored, I thought, 'Oh, my God, we need two runs, and I've got to keep throwing my finger down and get outs,' " Alfonzo said.
The Giants got those two runs right away off Angels starter Kelvim Escobar (5-8), as Randy Winn led off the bottom of the first with a single, went to third on Mark Sweeney's hit, and scored when Barry Bonds doubled down the left-field line.
Sweeney then scored on Steve Finley's groundout to second, and Cain had everything he needed for his assault on the history books.
"I felt good at the end of the first inning," he said. "I was just trying to get their hitters to help me out, and they did."
"He had good stuff," said Angels third baseman Dallas McPherson, the victim for two of Cain's career-high 10 strikeouts. "He worked both sides of the plate with a good fastball. He kept us off balance. You have to tip your cap."
By "good stuff," McPherson meant a mid-90s fastball coupled with a curve decent enough to keep the Los Angeles hitters from sitting on the heater.
"I got a good combination with the pitcher today," Alfonzo said. "Everything I threw down, he threw the pitch.
"Everything was working today, the fastball, the curveball."
But especially the fastball.
Alou said he really began thinking about the possibility of the no-hitter when Vladimir Guerrero was in the batter's box.
"The big guy was swinging and missing and fouling off his fastballs," Alou said. "He threw enough breaking balls and changeups, but he overpowered him with his fastballs."
Cain was at his most overpowering in the seventh, when he struck out the side. No. 5 hitter Mike Napoli went down swinging, then Kendry Morales and McPherson in succession watched strike three whiz past.
By that time, Cain had thrown 112 pitches.
"You really hate to see a kid get that many pitches and not get a no-hitter," Alou said. "We decided until they got a hit, he was going to stay in there."
That was fine with Cain, who will get an extra day's rest before his next start because the Giants have an off-day between completing the Angels series on Wednesday and starting one with the A's on Friday.
"At that point [the end of the seventh], I felt good and I was going to keep going until they dragged me off the mound," Cain said.
The 21-year-old righty certainly looked fine going into the eighth. He got Guerrero to fly out to left, then caught Garret Anderson looking.
That brought up Figgins, who worked the count full. Because the speedy center fielder had already walked twice, stolen two bases and scored a run, the Giants, nursing a one-run lead, weren't about to give him another free pass.
"At that time of the game, you go with the best pitch you've got," Alfonzo said.
So Cain came after Figgins with a fastball, and Figgins laced it up the middle.
"I made a good pitch and he hit it," Cain said of pitch No. 128 on the night. "In that situation you have to make him hit it."
The Giants' last no-hitter was thrown by John "the Count" Montefusco on Sept. 29, 1976, in Atlanta.
As soon as Figgins got his hit, the Giants bullpen got busy, but Cain, due to lead off the ninth inning, stayed in and got Orlando Cabrera to pop out to Vizquel at shortstop to end the threat.
"You always feel bad anytime you go into the eighth or ninth inning and they break it up," Vizquel said. "It's like a stab in your heart."
Cain's night ended with just the one unearned run allowed on one hit, four walks and 10 strikeouts.
Benitez came on to work the ninth, and after giving up a two-out single to Napoli, he got Morales to fly out to center to get save No. 5 on the year.
For Cain, it wasn't even his best outing of the year. He threw a complete-game one-hitter while blanking the A's May 21 in Oakland.
That suggests this won¹t be the last time he flirts with a no-hitter.
"He has no-hit stuff, no question about it," Alou said. "It's just a matter of time and getting that slider and curveball a little closer where they have to swing at it. Right now, hitters are taking his breaking balls because they are far from the strike zone."
"He still has to learn how to pitch," Vizquel said. "You can't have a 95 mph fastball all the time. When he really learns how to pitch and knows what to do with the ball, he'll be one of the best."