At the bottom West Ham United eased their relegation fears when they ended a five-match losing streak with a 1-0 victory over third-from-bottom Swansea City at London Stadium.
Second-from-bottom Middlesbrough's hopes of beating the drop are slipping away though after they could only draw 0-0 at home to Burnley, stretching their winless run to 14 league games.
Elsewhere, Southampton won 1-0 at West Bromwich Albion. In a potentially tricky visit to the sun-drenched south coast, Chelsea started in dominant fashion and led when Diego Costa's effort deflected in off the unlucky Smith.
There was no luck about their second goal, however, with Hazard, one of the Premier League's outstanding attacking players, collecting N'Golo Kante's pass with a superb touch before searing past Artur Boruc and finishing from an angle.
The in-from King pulled a goal back for the hosts but the visitors had too much quality and sealed the win when the often unheralded Alonso curled home a breathtaking free-kick to cap an impressive personal performance.
"When you have this type of opponent who is in good form and wants to catch you, it is important to have a good answer. This is a good answer," Conte told the BBC.
"There are seven games to go and in England it is not easy, there is a lot of pressure. It's normal to have a good pressure [after Spurs won]."
Tottenham chalked up a sixth successive victory, Dele Alli scoring a superb goal - his 16th of the season in the league - and Eric Dier doubling the lead before Son's brace.
Spurs will be hoping Manchester United, Chelsea's next opponents, can do them a favour by beating the Blues.