The 16-year-old American confirmed her status as the rising star in women's figure skating with a spotless free skate that earned her top marks and a personal best overall winning score of 218.33.
Japan's Fumie Suguri, fourth at the Olympics and twice a world championship bronze medallist, took the silver with 209.74 while a shaken Cohen settled for the bronze on 208.88.
"Going into my first worlds I just wanted to have fun," said Meissner, third entering the free skate.
"But I hit my first jump and told myself, I can do this.
"It definitely felt like it was a personal best; it blew all my other performances out of the water.
"This was definitely the best ever."
With Olympic gold medallist Shizuka Arakawa and defending champion Irina Slutskaya not competing in Calgary, Cohen was installed as the gold medal favourite coming in the worlds.
But once again, Cohen failed to deliver, cracking under the pressure of the big moment.
After a silver medal at the Turin Olympics, a pair of runner-up results at the worlds and four second place finishes at the U.S. championships, Cohen had finally looked poised to shed her unwanted tag of figure skating's perennial bridesmaid and make the final step to the top of the podium.
First among the last group to skate, Cohen got her routine to Romeo and Juliet off to an unsteady start and never found her rhythm and confidence.
Shaky on almost every jump, Cohen crashed to the ice on her final triple Salchow and then as the music finished stood dejectedly at centre ice, head bowed knowing she had let another gold medal get away.
"Years ago I use to cry but I think I've used all my tears up," said Cohen, in what might have been her final competitive performance having indicated she is contemplating a move from the rink to the stage. "It's not going to help me to cry. It's going to help me to figure out what went wrong.
"I fought, I struggled out there.
"It's frustrating and disappointing but I know I gave it my best effort so I have to be satisfied with that part."
Competing at her first world championships, Meissner displayed the icy cool, veteran poise and mental toughness Cohen has lacked throughout an unfulfilled career.
While Meissner's playful free skate to the Queen of Sheba may have lacked the pure artistry and passion of more seasoned performers, it packed an athletic wallop that was unrivalled by any of her opponents as she cleanly landed seven triple jumps, including two triple-triple combinations.
"Last year I wasn't old enough to come to worlds and today I was standing on the podium, I was thinking it's so strange," said Meissner. "I've come a long way."
Crashed but not burned
She's Cohen the distance