As well as Son and Kane, Alli also proved a constant pain to the Everton midfield and defence.
But with 26 minutes gone, Son timed everything right when Serge Aurier's scuffed shot fizzed across the box and he steered the ball home from close range.
Gerrard won the first of his Player of the Month awards in March 2001, and his final one came 13 years later.
It took just two minutes of the second half for the game to spring back into life.
Colombian striker Falcao was again ruled out by a muscle injury that sidelined him for cup wins over Yzeure and Nice, and Monaco couldn't break down the league's meanest defense without their top scorer.
It was a third straight goalless draw involving Chelsea in all competitions - and a fourth in the team's last seven matches. Everything Kane touches turns into gold, which his 98th, and record-setting Premier League goal, was evident of. "This way he's going to break all the records in the Premier League and in England, and it's fantastic because he helps the team every week".
"Tottenham can beat anybody by a lot of goals but they should have had to work a lot harder than they did".
This was Tottenham's biggest margin of victory in a game against Everton since a 10-4 win in October 1958. [You have to] play your way back into the game and be professional about it.
According to the Daily Mail, there are 34 Premier League players who are earning more than the 24-year-old, including West Ham's Javier Hernandez (£115,000 per week), Crystal Palace's Christian Benteke (£120,000 per week) and Liverpool's Daniel Sturridge (£150,000).
"That makes him a special player. Hopefully I can get to the 100 as soon as possible".
Sam Allardyce: "Maybe I have a bit of responsibility by playing too much attacking-minded players and not as many defending-minded players".
With Leicester vulnerable following Ben Chilwell's dismissal in the second half at Stamford Bridge, it was the ideal moment for Morata to silence the critics beginning to question whether he is an adequate replacement for Diego Costa.
Kane's goals have come in only 135 games, while Sheringham took 237.