Martinez's team were in UEFA Europa League action against Dynamo Kiev on Thursday and, coming into this meeting at Goodison Park, had won just two of their eight league matches that had immediately followed a European game.
However, they brushed Newcastle aside to seal only their second win in 13 league outings and ease their relegation fears.
Newcastle keeper Tim Krul allowed James McCarthy's low shot to creep in, before Romelu Lukaku doubled the lead from the spot following Yoan Gouffran's foul on Aaron Lennon.
Fabricio Coloccini was then dismissed for a foul on Lennon before Ross Barkley rounded off the scoring in stoppage-time.
"It's taken us a long time this season to perform after a European game," Martinez said. "The squad reacted in a fresh manner today.
"It was a big game for us and sometimes that can bring extra pressure, but we started the game with great intensity.
"We have strong competition for places - players are ready to perform.
"On Thursday we found the enjoyment we need. We have top individuals. The mindset today was of real desire to show what we can do.
"We want to perform as we did today in all of our final nine games. We now go to Kiev and we are desperate to get through to the quarter-finals of the Europa League."
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