The Dutch keeper entered the fray after club skipper Hugo Lloris suffered a hamstring injury in the 35th minute of the game at Goodison Park.
Vorm made a telling contribution when he denied Gerard Deulofeu from giving the Toffees a 2-0 lead in a one-on-one chance just before half-time.
"These are the moments that I have to be ready for and I don't get fazed by it with the experience that I have," he told the club's official website.
"You always have to keep in mind that something might happen, it hasn't in the last few seasons, it did here. You can see again that something can change in a minute.
"It always strange when you have to come on in these circumstances, but if you can make an impact in a positive result then happy days!"