As late summer sun settled above Tottenham’s symbolic golden cockerel, even the single-minded manager Ange Postecoglou could bathe in greater warmth and sustenance from a support that has been highly critical of the club’s errant start to the season.

A win for enterprising Spurs, thanks to goals from Dominic Solanke – his first for the club – Brennan Johnson and James Maddison earned the three points. It was an afternoon of character from the hosts who responded eagerly after conceding a goal when Bryan Mbeumo put Brentford in front with a minute gone.

This mark of fortitude should provide increased faith from the fans towards their manager, who was quick to acknowledge them at the climax.

Related: Tottenham v Brentford, Liverpool v Bournemouth and more: football clockwatch – live

In a tetchy buildup, Postecoglou was stressing bigger pictures, recommending yoga sessions for over-zealous supporters contemplating four points from four Premier League games before a very timely victory. This, in tandem with a dramatic escape act at Coventry last Wednesday in the Carabao Cup, following the obvious disappointment of home derby defeat to Arsenal, the spikier questions asked were answered against Brentford.

These included the perceived lack of organisation when facing set pieces, and a frustrating lack of end product in the final third. The latter aspect was addressed with well-taken goals by Johnson and Maddison in particular, with the club’s record signing, Solanke, netting his maiden goal.

Postecoglou’s side pressed extremely hard, forcing Brentford into regular mistakes.

Once recovered from the blow of conceding after a mere 22 seconds, when Mbeumo hooked a superb volley into the roof of the net from a Keane Lewis-Potter cross, an uncharacteristic loose pass from Ethan Pinnock was snapped up by Maddison inside the Brentford penalty area. The midfielder’s shot was only parried by the visiting goalkeeper, Mark Flekken, with the grateful Solanke casually stroking the ball home.

Spurs added a second when Heung-min Son funnelled a pass to Johnson, who made a yard of space beyond Nathan Collins to fire low into the corner of the Brentford net from an acute angle.

With six minutes to go, the ever-influential Son caught Brentford off-guard, supplying Maddison who curved the ball delightfully over Flekken.

“It wasn’t an ideal start but we knew Brentford would be pretty aggressive,” said Postecoglou.

“We love that part of the game and we brought that intensity and energy and caused them a lot of problems. We fully deserved the win. Everyone really contributed to a strong performance.”

The Brentford head coach, Frank, was singled out for praise last weekend from the sage Pep Guardiola, as the Bees pushed champions Manchester City close. Indeed, Frank’s recent off-the-cuff admission that he is capable of managing any club in the world, is an indication of a stirring, quiet ambition within the likeable Dane.

With a number of key men, such as Yoane Wissa, Rico Henry, Igor Thiago and Mathias Jensen out from his preferred line-up, is, at the same time, a realist. They are getting their theoretically tougher games out of the way, having already visited Liverpool and Manchester City. Despite this loss, there remains much to admire about Brentford’s intent.

“I saw a very good Spurs team who performed very well,” said Frank – who was booked for protesting at a perceived handball by the home keeper, Guglielmo Vicario, outside the penalty area. “We started fantastically, then Tottenham were on top.

“We had four big chances to equalise. We go to every away ground and try and win. We were playing a team fully firing out there and we have five very experienced  players out. That’s just perspective, not moaning.”

• Download the Guardian app from the iOS App Store on iPhone or the Google Play store on Android by searching for 'The Guardian'.

• If you already have the Guardian app, make sure you’re on the most recent version.

• In the Guardian app, tap the Menu button at the bottom right, then go to Settings (the gear icon), then Notifications.

• Turn on sport notifications.

Tottenham’s fans were quick to salute Johnson, who has closed down his Instagram account after social media abuse. A late Carabao cup winner against Coventry was followed by an excellent display here, in partnership up front with Solanke. One that has significant promise.

“Brennan works really hard for our team and is a big part of or club”, Postecoglou said. “You can see how much he cares. Every footballer goes through difficult moments and it gives you perspective, he’ll know what’s important to him.”

A day of evident relief for Postecoglou too – yoga or not – where you sense Tottenham can now properly move forward.