The game suddenly burst into life, with Gayle forcing Hugo Lloris into a save at his near post, but Newcastle's positive response soon fizzled out.
Moussa Sissoko was booed as his return to St James' Park ended with Son Heung-min taking his place before the hour mark, and Tottenham soon made their extra man count.
The club's last Premier League game came against Spurs, with the Magpies already relegated and the north Londoners aware that a victory would see them finish above Arsenal.
Some neat interplay between Harry Kane and Christian Eriksen on the edge of the penalty area saw the ball drop for Ben Davies and the full-back found the net. The Blues will be hurting after their opening-day humiliation at the hands of Burnley.
- Shelvey has been sent off twice under Rafael Benitez at Newcastle, more than any other player.
The referee had no other option than to issue a clear red card to the England global.
He has also played 13 times for the Liverpool first team, but after just two FA Cup appearances in the last campaign he may now be seeking regular Premier League football.