Swift was named Best U.S. Act and claimed Best Video for "ME!", featuring Brendon Urie, while Eilish took home Best New Artist and Best Song for "Bad Guy".
K-Pop superstars BTS also had a good night at the ceremony in Seville, Spain, picking up Best Live Act and Biggest Fans.
Other winners included Shawn Mendes (Best Artist), Halsey (Best Pop) and Green Day (Best Rock), while Liam Gallagher was presented with the inaugural MTV EMA Rock Icon honour and graced the stage to perform his new single, "Once", as well as Oasis classic "Wonderwall".
The full list of winners is: