The 19-year-old midfielder, pursued by Liverpool but grabbed by Spurs for what now looks a bargain five million pounds ($7.13 million) in February, struck after 84 minutes to put the visitors 2-1 ahead.
Alli, who spent last season on loan at lower league side Milton Keynes Dons, evoked memories of White Hart Lane greats Glenn Hoddle and Paul Gascoigne with the skill he produced.
Standing 25 metres out, he controlled a header from Christian Eriksen before delicately flicking the ball over his head to beat Palace defender Mile Jedinak and then smashing a low volley past keeper Wayne Hennessey.
"It all came naturally," Alli told Sky Sports television after producing a contender for goal of the season. "It was a great ball and I just took a touch and hit it.
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"I didn't have time to think. I didn't know what to do with my celebration."
A Jan Vertonghen own goal put Palace in front before Spurs hit back through Harry Kane, Alli and another superb long-range strike by substitute Nacer Chadli with almost the last kick of the game.
"It was a fantastic goal (by Alli) and it showed his quality," said Spurs manager Mauricio Pochettino. "It is a goal that will be seen around the world on television.
"We knew he was a player of unbelievable potential but today he showed unbelievable maturity and quality."
Kane said: "I've never scored a goal like that and I haven't seen one as good as that for a long time."
Palace manager Alan Pardew also heaped praise on Spurs teenager Alli.
"It was a great goal," said Pardew. "It was horrible to watch and I don't often say that about a beautiful goal.
"As soon as he flicked the ball over his head I feared the worst. It was a great moment for him and he is a great talent."
Hodgson has already handed Alli four England caps this season, and with one stunning goal for his country already against France in November, he is now a serious option to start at the Euros in France in June.
(Editing by Tony Jimenez)
