Davies added Tottenham's second with 20 minutes remaining, finishing a slick move with a composed finish beyond Newcastle goalkeeper Rob Elliot, Eriksen again the provider.
Gayle forced a near-post save from Hugo Lloris in the immediate aftermath, but opposite number Elliot had to make a fine 52nd-minute block to deny Harry Kane the opening goal.
Newcastle United vs. Spurs predicted lineups, TV news and preview
Tottenham controlled possession but Gayle threatened in behind and went down in the box under contact from Kyle Walker-Peters, making his Spurs debut at right back with Kyle Walker sold to Manchester City and Kieran Trippier out with an ankle injury, only to see the flag raised for offside.
The Toon midfielder was given his marching orders in the second half of the Premier League clash on Sunday after leaving one on Alli, causing widespread confusion over his freakish decision. Christian Eriksen and Dele Alli support Harry Kane.
And to nobody's surprise - except Shelvey's - Mariner brandished a straight red card. Eric Dier plays, as does Moussa Dembele, while there is also a start for former Magpie Moussa Sissoko.
The brain-fade derailed Newcastle's momentum and any chance of pulling off an upset against last years Premier League runner-ups.
Accoltellano due minorenni per una sigaretta negata: fermati due ragazzi a Ischia
L'altro ha ricevuto tre fendenti tra zigomo e coscia, con una coltellata che avrebbe potuto recidergli l'arteria femorale. Sono le accuse per cui sono stati arrestati due 19enni della "Napoli bene" in vacanza ad Ischia .