This might have been Mauricio Pochettino’s most significant half-time team talk in his three years at Tottenham and it might, just might, have breathed life back into the Premier League title race.

Without their talisman Harry Kane, forced into two late first-half alterations, and with a goalless draw at one of the top flight’s toughest grounds beckoning, Pochettino ditched his usual interval routine of analysing the first-half highlights. Revamping a beleaguered Spurs and altering their system, he returned to the bench unusually early alongside his assistant Jesús Pérez, leaving his players to contemplate the task ahead.

The response to their adversity – Victor Wanyama was forced off with a back injury and Harry Winks taken off on a stretcher and given oxygen on the way to hospital after going over on his ankle – was stunning. With Eric Dier, who seamlessly switched from a position in the back three to one in front of the defensive line, and substitute Mousa Dembélé directing traffic, Tottenham’s monopoly on second-half possession paid rich dividends as Chelsea’s lead was cut to seven points with nine games remaining.

First, Dier kept his composure to steer the ball home after Burnley failed to deal with a Christian Eriksen corner midway through it. Then, 11 minutes later, victory was sealed when Son Heung-min converted one of half a dozen other good chances in the final quarter, emerging at the far post to sidefoot in after Dele Alli tightrope-walked the offside line.

“It was a massive three points for us to still believe and fight for the title,” said Pochettino. “It’s always difficult the first game after the international break but it was a very professional performance. We showed great belief, character and faith and that made me proud.”

Of the interval intervention, he said: “It was a big hit for us, for the team, so it was very important when the players got in to switch on and change things. We changed formation. The team needed lifting. It was a very concerning moment but the reaction was really good.”

Tottenham, with a back three selected to combat Burnley’s physical threat down the middle that often became a five early on, struggled to create chances before the break.

Tottenham’s Harry Winks is taken off on stretcher. Photograph: Jason Cairnduff/Reuters

With Chelsea trailing to Crystal Palace, a muted anticipation pervaded the travelling support but all their team could create in the opening 45 minutes was a single opportunity for Alli. Having played a major role in a quicksilver counter from deep, he, arrived right on cue to seize upon the rebound after Tom Heaton parried Eriksen’s low cross, yet somehow lifted over the top with the goal at his mercy.

When several others were squandered at the start of the second – Moussa Sissoko, another replacement, slashed wide when well-positioned and Heaton foiled Vincent Janssen and Ben Davies in quick succession – time was running out.

But Eriksen’s corner travelled to the back post and when Jeff Hendrick failed to clear, Dier controlled with his first touch and stroked in with his second.

With the game stretched opportunities came by the bucketload: Son hit the side-netting after Eriksen robbed Hendrick in midfield before anticipating Alli’s low centre 13 minutes from the end. Had Alli’s delightful dink put a finer sheen on the result there could have been few objections.

The result also has significance at the other end of the table with Burnley – momentum stalled by hosting two of their past seven league fixtures – now five points outside the relegation zone.

However, despite this and a failure to test Hugo Lloris in the Tottenham goal, their manager, Sean Dyche, remained buoyant: “We know we have been on a tough run. We are not delusional, we understand the nature of the division, and there’s no such thing as done deals in the Premier League.” How Tottenham hope that last reflection rings true.