Kerber, 28, won 6-3 4-6 6-4 in New York to add the US Open to her victory at the Australian Open in January.
Pliskova's semi-final win over Serena Williams had already ensured the German will top the new rankings on Monday.
"All my dreams came true today and I'm just trying to enjoy the moment," said Kerber.
"It's incredible. I'm standing here with a second Grand Slam trophy and it means so much to me."
Kerber was appearing in her third Grand Slam final of 2016, and the German played with the authority of a world number one in waiting.
Pliskova, 24, went into the final with a WTA Tour-leading 447 aces this year and on an 11-match winning streak that included victory over Kerber in last month's Cincinnati final.
The Czech had never been past the third round of a major before this tournament and made 17 unforced errors in the first set, but fought back with 17 winners in the second before powering 3-1 ahead in the decider.
It looked as though Kerber's athleticism and defensive skills would not be enough, but she levelled at 3-3 and then roared as a blistering forehand winner helped her move ahead once again.
At 4-4 in the final set it came down to a test of nerve, and Kerber's was rock solid as she held impressively before Pliskova fell 0-40 behind and blazed a forehand wide on match point.
"It's always tough to play against her," said Kerber. "I was trying to stay in the moment, be aggressive, I was just trying to enjoy the final. It's an amazing stadium.
"It means a lot to me. When I was a kid, I was always dreaming to be the number one player in the world and to win Grand Slams, and today's the day."
Pliskova said: "I found out I can play my best tennis on the big stages. She proved she's the world number one. I knew it was going to be difficult, but I found myself some power in the second set."
Kerber is the first German to win the US Open since Steffi Graf in 1996 and her ascent to the top of the rankings is the result of a spectacular year.
She began 2016 ranked 10th in the world after failing to get past the third round of any of the Grand Slams in 2015, but Saturday saw her claim a Tour-best 54th win of 2016.
Kerber won her first major titles in Australia and the US, as well as reaching the Wimbledon final, where she lost to Williams, and the Olympic final, where she lost to Monica Puig.
The German began the season with a shock win over Williams in Melbourne, which was only possible after she had saved a match point against Japan's Misaki Doi in the first round.