New Everton boss Frank Lampard was looking to ease worries about his side being dragged down closer to the relegation scrap.
They took the lead in the 36th minute through a Jamal Lascelles own goal, but when Mason Holgate scored an own goal just a minute later it was all square.
Newcastle played with intent in the second half and got their reward when Ryan Fraser put them in front in the 56th minute and Kieran Trippier scored a third with ten minutes left.
Former Premier League midfielder Lennon feels that Newcastle fully deserved to take all three points as they were the better team.
And he insists that the way Everton reacted in the second half was not great.
“No question the better team won. The turning point was Newcastle’s first goal”, Lennon said on BBC Radio 5 live.
“Everton’s reaction second half wasn’t great.
“All the power, all the poise, all the quality came from Newcastle, got the two goals and fully deserved their win.
“There is a feel-good factor around the stadium and you can see in the players they got stronger as the game went on – the crowd played a huge part in that.”
Newcastle are now a place and two points outside the relegation zone and just one point and one place behind Everton, though the Toffees do have a game in hand.
