The Magpies, promoted as winners of the Championship last term, had captain Shelvey sent off early in the second half for standing on Dele Alli.
The Spurs attacker then put his side ahead with a close-range finish before Ben Davies finished off a neat move for Tottenham's second.
It was a harsh re-introduction to life back in the Premier League for Newcastle, who were relegated from the division at the end of the 2015-16 season.
Rafael Benitez's side did not really threaten Hugo Lloris in the Tottenham goal until late on, Christian Atsu forcing the goalkeeper into a low save and Ciaran Clark going close with a volley from 12 yards.
Afterwards, Benitez was asked about whether he would have a meeting with owner Mike Ashley about signing players.
"I don't know." When he was asked if it was up to Ashley whether they met, he said "yes". and then he added: "I am concentrating on my job and my players."
Benitez agreed that Shelvey deserved his red card: "The sending off changed everything. He made a mistake. Hopefully he will learn from it. He has apologised but that changes nothing now."