The Belgium striker scored both goals in a 2-0 win over West Ham to provide a fitting send-off for the Toffees boss - heading for Manchester United in the summer - after he has stood on the touchline in the blue corner of Merseyside for 11 years.
The sixth successive home league victory against a West Ham side who seemed to have no intention of spoiling the party also guaranteed Everton finished above Liverpool for the second successive season for the first time in the top flight since 1937.
In his programme notes, club captain Phil Neville, who is leaving Everton as a player this summer, said he had never met a harder working man than Moyes - which is some tribute from a man who spent 11 years with Sir Alex Ferguson at United.
And the players started as if they wanted to give their manager the performance his excellent long-term work deserved, taking only six minutes to break the deadlock.
In a crisp passing move, the ball was moved in from the left touchline from Leighton Baines to Marouane Fellaini, the two players most likely to be coveted by Moyes for his new dawn at United, and then on to Steven Pienaar who teed up Mirallas to drill home from the edge of the area.
The Scot was all smiles and double fist-pumps again on the hour when Pienaar released Mirallas to run at the defence and his shot deflected up off James Collins and past Jaaskelainen.
Even West Ham's on-loan Liverpool striker Andy Carroll could not but a dampener on proceedings, hitting the post with a late header.
After the final whistle the squad formed a guard of honour for Neville and then Moyes, who received the biggest cheer of the afternoon.
The manager walked to the centre-circle waving to the crowd but looked like he did not know quite how to react as chairman Bill Kenwright watched on from the directors' box with a tear in his eye.