Dawson received 420 of 539 votes in voting announced by the Baseball Writers' Association of America, 15 more than the 75 percent necessary to gain election. The eight-time All-Star outfielder had fallen 44 votes short last year.
"It was well worth the wait. I can't really describe the elation," Dawson said during a telephone conference call. "If you're a Hall of Famer, eventually you're going to get in, no matter how long it takes."
Blyleven had 400 votes (74.2 percent), up from 338 last year, and the pitcher will likely get in because he has two more tries on the BBWAA ballot. The highest percentage for a player who wasn't elected in a later year was 63.4 by Gil Hodges in 1983, his final time on the ballot.
"Hopefully, next year will be my time," Blyleven said in an interview on MLB Network.
Alomar received 397 votes (73.7 percent) in the second baseman's first appearance and was followed by pitcher Jack Morris with 282 (52.3 percent), a big rise from his 237 last year.
"I feel disappointed, but next year hopefully I make it in," Alomar said at his home in New York. "At least I was close."
Cincinnati shortstop Barry Larkin, also making his first appearance, was on 278 ballots (51.6 percent), followed by reliever Lee Smith at 255 (47.3 percent) and slugger Edgar Martinez at 195 (36.2 percent). Martinez, on the ballot for the first time, is viewed as an early test of how voters will receive players who were primarily designated hitters.
Mark McGwire received 128 votes (23.7 percent), 10 more than last year and matching the total from his first two times on the ballot. Eighth on the career list with 583 homers, he has been stigmatized since evading questions from Congress in 2005 about steroids use.
McGwire was hired in October as the St. Louis Cardinals hitting coach and is expected to hold an introductory news conference at some point.
Dawson will be inducted July 25 at Cooperstown along with manager Whitey Herzog and umpire Doug Harvey, elected last month by the Veterans Committee.
Dawson hit 438 homers in a career that spanned from 1976-96. Nicknamed "The Hawk," he was voted NL Rookie of the Year in 1977 with Montreal and NL Most Valuable Player in 1987 with the Chicago Cubs, the first member of a last-place team to earn the honor.
A victim of owners' conspiracy against free agents after he left the Expos, Dawson signed a blank contract with the Cubs during spring training. Then-general manager Dallas Green filled in the dollar amount of $500,000, making Dawson the second-lowest paid regular on the team.
Dawson stayed with the Cubs through 1992, then spent two seasons apiece with Boston and Florida. He had a .279 career average with 1,591 RBIs and 314 steals, playing through 12 knee operations.
He is one of only three players with at least 400 home runs and 300 stolen bases, joining Barry Bonds and Willie Mays.
The close calls for Blyleven and Alomar marked the first time in BBWAA balloting that two players fell fewer than 10 votes short in one year.
Alomar received the most votes of any first-year candidate who wasn't elected.
Next year's ballot also will include newcomers Rafael Palmeiro, Juan Gonzalez, Larry Walker, Jeff Bagwell, John Franco and Kevin Brown.