Spurs looked to be heading for their first league draw of the season at Wembley but Son's 83rd-minute goal earned Mauricio Pochettino's men a hard-fought 1-0 win over Newcastle and enabled them to leapfrog Manchester City, who play on Sunday.
Chelsea beat bottom side Huddersfield 5-0 thanks to two goals apiece from Higuain and Eden Hazard and a late header from David Luiz as they returned emphatically to goalscoring form.
Tottenham are now just four points behind leaders Liverpool, who are in action at West Ham on Monday, but just as significantly they consolidated their position in the top four after their 19th win in 25 matches.
Spurs enjoyed more than 70 percent possession but faced a dogged Newcastle, buoyed by a stunning 2-1 win over Manchester City in midweek that carried the Magpies five points clear of the relegation zone.
An incredible clearance off the line from Fabian Schar denied what seemed a certain goal for Christian Eriksen and Fernando Llorente then looped a golden headed chance high and wide.
But Son again stepped up to the mark, just as he did with an equaliser against Watford in midweek, to compensate for the injured Harry Kane's absence with his 14th goal of the season.
Hazard can leave Chelsea if he wants, says Sarri
The South Korean had a helping hand from Newcastle goalkeeper Martin Dubravka, who let Son's powerful effort slip beneath his grasp to undo all his side's good work.
"It is a massive result to be in a very good position in the table," said Pochettino. "We don't need to be in some position like today to convince ourselves about our capacity or potential. We believe in ourselves."
And the Argentine lauded Son's stamina since he returned from the Asian Cup.
"Sonny is like a battery that you have that you work, work, work, work but when the battery is gone, it's gone," he said.
Chelsea manager Maurizio Sarri admitted before the match against bottom side Huddersfield that he had found it hard to get any rest since Wednesday's humiliating 4-0 defeat at Bournemouth.
His side, seeking to avoid a third straight Premier League defeat, went ahead in the 16th minute through Higuain and doubled their lead with an Hazard penalty on the stroke of half-time.
Both players scored again midway through the second half and Luiz made it 5-0 with a late strike as Chelsea returned to the top four at the expense of Arsenal.
Higuain, 31, was signed on loan until the end of the season from Juventus to help the 2016/17 champions rediscover their sharpness in front of goal.
Chelsea agree Higuain loan from Juventus
Elsewhere, struggling Fulham were unable to recapture the spirit of their dramatic midweek comeback against Brighton, losing 2-0 to Crystal Palace.
Wolves consolidated their position in seventh place by beating Everton 3-1 at Goodison Park, while Southampton conceded a penalty deep into added time to draw 1-1 at Burnley. The match between Brighton and Watford finished goalless.
In the late kick-off, Cardiff are playing at home for the first time since the disappearance of a plane carrying new signing Emiliano Sala from France.
Defending champions Manchester City, five points adrift of leaders Liverpool, host Arsenal on Sunday, with Manchester United travelling to former champions Leicester.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ