Swansea, on the other hand, suffered their first defeat under new manager Carlos Carvalhal, and they stay rooted at the bottom of the table, four points adrift of safety.
Spurs revealed on Friday that the England global had been suffering with an illness and, although he has travelled, he has not been deemed fit enough to start at Liberty Stadium.
Tottenham was fortunate not to have Davinson Sanchez sent off early in the second half, when he fouled Martin Olsson when already on a booking. Dele Alli has recently rediscovered his touch, but he's still not where he was last season.
However, after helping his side to come from behind to win at Vicarage Road - they trailed 1-0 with just four minutes remaining - McBurnie is hopeful they have got what it takes to get themselves out of trouble.
Carvalhal said: 'I will not start talking about the referees.
"There are two points I can talk about".
Before their 0-3 win at Burnley, Mauricio Pochettino's men had failed to win in five consecutive away games, which is part of the reason for their slide down to sixth place in the table.
"I understand it's a mistake".
"He is so important for us", Pochettino said of Son.
The 21-year-old told the club's official website, www.swanseacity.com: "Belief and confidence are some of the main things we need to re-install in our game in 2018".
With Alli returning to form over the past few games and Harry Kane still finding the back of the net for fun, there's no reason why Tottenham couldn't end the season with at least one piece of silverware.
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