Newcastle had been competitive at St James' Park but, after Shelvey's dismissal, Alli tucked away Christian Eriksen's excellent cross to break the deadlock before Davies finished off a fine team move.
Tottenham Hotspur have confirmed on their official website that four first-team players are set to sit out of the club's 2017-18 Premier League opening fixture against Newcastle United on Sunday. He was later joined on the bench by Florian Lejeune following a heavy challenge from Harry Kane that resulted in a booking for the Spurs striker.
Jacob Murphy and Mikel Merino are named among the substitutes on the bench, but could make their debuts for Newcastle.
Newcastle scored 26 goals from set-pieces in the Championship last season.
Moscow mule copper mugs may be toxic, officials say
When the copper or copper alloys come into contact with food or liquid with a pH below 6, the copper can leach into it. A different interior should line the inside of the cup, such as stainless steel and nickel.
Sissoko was taken off after 57 minutes, a tactical swap for Son Heung-min, and within three minutes Spurs took the lead. Dele Alli bagged the opener, on the stretch, the midfielder put the ball into the back of the net with an hour played.
Nine minutes later, Eriksen ran into the area but was beaten to the ball by Davies, who tucked a close-range finish under goalkeeper Rob Elliot. They were wonderful last year supporting the team and they will be the same this year.
Kane was denied his 100th goal for Spurs by the foot of the post in the 90th minute.
Pochettino said last week that Walker-Peters was not ready to play in the Premier League but he claimed he had been bluffing to avoid putting pressure on the youngster.