It was a good result for a performer who admitted she was too excited to sleep the night before the ceremony, and said was shaking after walking past a gaggle of photographers on the red carpet.
Minaj proved a confident if conventional host for the show at Glasgow's SSE Hydro arena, and she also took home the prize for best hip-hop artist.
"I've been learning so much about your beautiful country and culture ... I've pretty much become Scottish," Minaj said. She illustrated it by rapping about whiskey and shortbread and singing a snippet of The Proclaimers' anthem "500 Miles."
Minaj's more provocative side was kept under tight control. There were writhing dancers during a performance of her bum-centric hit "Anaconda," a putt into derriere-shaped mini-golf hole in tribute to Scotland's love of golf, and a couple of F-bomb obscenities directed at — of all things — an animatronic dinosaur. But on the whole the event stuck to a standard awards-show script.
Beyonce did not appear as widely rumored, and Scottish DJ Calvin Harris had to pull out due to illness. But thousands of young Scottish music fans in the arena — and a global TV audience — saw a high-energy show featuring performances from acts including Ed Sheeran, Alicia Keys, Enrique Iglesias and U2, who brought their own string section.
Rising talent was represented by the likes of crunchy British rock duo Royal Blood and singer Charli XCX, while former "Baywatch" star David Hasselhoff got a rousing cheer when he took the stage in a kilt.
Winners of the awards are selected by fans across the continent. The EMAs are held in a different European city each year.
Ubiquitous boy band One Direction won three awards, including best pop act. Katy Perry and Australian punk-poppers 5 Seconds of Summer each won two, and wayward heartthrob Justin Bieber was named best male artist.
None of those acts was on hand to accept their prizes in person.
Linkin Park won the rock category, and Chinese singer Bibi Zhou was proclaimed best worldwide act.
The awards, founded in 1994, adopted a time-travel theme for their 20th anniversary. Giant balloons of the planets floated in the arena, and Grande performed her song "Break Free" from a flying pod while wearing a white mini-dress reminiscent of the animated TV show "The Jetsons."
But there were few of the unscripted-feeling moments that made past shows stick in the memory — Kanye West crashing the stage after losing in 2006, Miley Cyrus smoking a joint in Amsterdam last year.
Even former bat-chomping hell-raiser Ozzy Osbourne — introduced by guitar hero Slash as a man who "scares the hell out of most people, and all bats" — seemed an elder statesman as he accepted a Global Icon accolade.