Miss Gutierrez, 21, then had her crown removed and handed to the real winner - Miss Philippines.
Pia Alonzo Wurtzbach appeared stunned, as Miss USA turned to her and mouthed: "I think you've won."
The women did their best to take the news with dignity. But the reaction of fans in Colombia has been less than gracious, with many expressing anger at the blunder.
The country's president, Juan Manuel Santos, has even weighed in, telling the country's Radio Nacional of his shock and disappointment. "To me, our queen is, and will remain, Miss Universe," he said. "They put the crown on her head. The photos are there to prove it. To me, as a Colombian, she is still Miss Universe."
Mr Harvey made a clumsy attempt to apologise on Twitter, emphasising how "regretful" he was to Miss Colombia - whose country he misspelt - and Miss Philippines, whom he referred to as "Miss Philippians".
"I want to apologise emphatically to Miss Philippians and Miss Columbia [sic]. This was a terribly honest human mistake and I am so regretful," he said.
Miss Wurtzbach described her crowning as "non-traditional - very 2015", while Miss Gutierrez, through her tears, said afterwards: "Everything happens for a reason." Yet the front page of El Tiempo, Colombia's leading newspaper, said: "Colombia was Miss Universe... for a few minutes."
And on Twitter millions of Colombians voiced disbelief and anger. "I'm in shock - what just happened there?" said Carolina Cruz Osorio, a model and television presenter, who was hosting the show in Colombia.
The event was marred by another bizarre twist when, afterwards, at least one person was killed and several injured when a woman with a toddler in her car repeatedly ploughed into pedestrians on the crowded Las Vegas Strip. Police say it was not an act of terrorism, but may have been an intentional assault.
It was the first Miss Universe since the show was thrust into controversy when Donald Trump, the then co-owner, called illegal immigrants "criminals" and "rapists".
His remarks, made in June when announcing his US presidential candidacy, caused the Spanish-language network Univision to pull out of a deal to televise the pageant.
The billionaire could not resist gloating over the latest fiasco. "Very sad what happened last night at the Miss Universe pageant," he said. "I sold it six months ago for a record price. This would never have happened!"