The 27-year-old Spaniard, who returned from a cruciate ligament injury in January, notched his first goal of the year in the 17th minute when he volleyed home Yakubu's cross.
Hull's heads were still spinning when Boaz Myhill saved Yakubu's poor penalty before midfield starlet Tom Cairney's strike dragged them level.
But Arteta struck again in the 39th minute before Richard Garcia fired past his own goalkeeper and Landon Donovan netted in his farewell appearance at Goodison Park, with Jack Rodwell adding the gloss.
In the 12th minute, Leon Osman robbed George Boeteng in the centre of midfield and fed Yakubu who sorted his feet out before poking the ball against the post with Myhill beaten.
After 12 months without an away win in the league, Hull boss Phil Brown opted to bus his side down to Merseyside on the day of the game.
But Nick Barmby appeared to still be on the coach when he allowed Arteta to drift into the Tigers box and net from Yakubu's 17th-minute cross.
After withstanding 16 more minutes of pressure Kamil Zayatte was penalised for bringing down Yakubu but the Nigerian's lazy penalty was blocked by Myhill.
Everton were immediately punished for the miss when teenager Cairney volleyed in a spectacular equaliser from 20 yards after the Toffees had failed to clear a corner.
Hull were buoyed by their first away goal of 2010 but, five minutes before half-time, Everton were back in front.
Arteta collected Steven Pienaar's clever back-heel in the area and slotted the ball into the bottom corner.
And things went from bad to worse for struggling Hull six minutes after the re-start when Garcia headed Arteta's clipped cross into his own net.
On-loan striker Donovan netted in the final scheduled home appearance of his loan spell, before Rodwell slotted home a fifth in the 86th minute.