Kluber captured 17 first-place votes and 169 points, narrowly edging out Felix Hernandez of the Mariners who earned the other 13 first-place votes and 159 points. White Sox LHP Chris Sale finished third with 78 points.
"I think I'm definitely surprised," Kluber said.
Kluber enjoyed a breakthrough 2014 season, his second full year as a starter, going 18-9 with a 2.44 ERA and 269 strikeouts in 235 2/3 innings. The right-hander led the league in wins, finished second in strikeouts, third in innings pitched and was third in ERA.
The 28-year-old Kluber was dominant down the stretch this season with the Indians (85-77), who fell just short of a postseason berth despite posting a winning record for the second straight year. He posted a 1.73 ERA after the All-Star break and won his last five starts, recording 54 strikeouts and a 1.12 ERA over that stretch.
When asked how he would celebrate the award, Kluber revealed plans far from flashy.
"Probably go home and give my daughters a bath," he said.
Hernandez said the tough loss will motivate him even more.
"I don't know what to say. That was tough,'' Hernandez said. "A little disappointed. Just give me more motivation to work harder and harder and be better next year."
Hernandez went 15-6 with an AL-leading 2.14 ERA and 248 strikeouts in 236 innings. He set a major league record when he pitched 16 straight games of seven or more innings and allowing two earned runs or less. It was a brilliant stretch from May to early August that put Hernandez in the lead for his second Cy Young award.
Information from The Associated Press was used in this report.