At around 4.34pm on Sunday Wayne Rooney announced to the home crowd that Louis van Gaal’s brave new Manchester United dawn had finally arrived.

That will be the hope, anyway. The moment in the opening half when the captain collected an errant pass from Tottenham’s Nabil Bentaleb and ran straight at goal, scattering Eric Dier before him with a body swerve before switching to ice-cold assassin mode and finishing beyond Hugo Lloris was surely the Van Gaal blueprint in microcosm.

United were now 3-0 up against Tottenham and had put on a high-octane display of hunger and pace and end product that suddenly made the Dutchman the wise man of Old Trafford.

Here, at last, was evidence of the crystallisation of the two p-words that form the Van Gaal mantra: process and philosophy. Those who have viewed the 63-year-old as a manager out of time because of the constant tinkering with formation and selection that had caused sluggish fare could now see the method to his masterplan.

Rooney said of his 13th goal of the campaign: “It was obviously a nice goal. A mistake by Bentaleb and I picked the ball up, saw that I had no team-mates around and I just went for it, attacking the defence. Thankfully I went through and scored.”

Here are words to gladden the hearts of all United fans: “I just went for it, attacking the defence.”

Rooney’s goal followed some rousing words on Saturday evening, as Marouane Fellaini said: “Last night the captain talked to the team about next season for the Champions League. It affected the team and it was an important speech.”

On a day which began with a story about him being knocked out in his kitchen, the buccaneering goal Rooney struck illustrated that he remains the street-fighter who can be the driving force of the post-Sir Alex Ferguson United.

This was what Sunday felt like – both a throwback to the Ferguson days of big-dipper football and the signpost to a fresh United that can bristle with intent and menace again. And it came against an opponent in Spurs who arrived posing a threat to Champions League qualification hopes but who left routed and six points behind a United side who now believe their second-placed crosstown rivals can be caught.

Of the champions, who are only two points ahead of United following the 1-0 defeat at Burnley, Rooney said: “We knew it was a big game, obviously with Manchester City losing on Saturday and Southampton drawing before we came out. It was a big game to take some points off Tottenham and these are three great points for us.

“We have played well a few times this season. Particularly in the first half, that was probably the best 45 minutes we’ve had all season. In the second half we knew we didn’t want to lose advantage of the three goals that we had, so we defended really well, we saw the game out and won.”

The Van Gaal vision is illustrated by Fellaini’s emergence as a key lieutenant. Against Spurs he threw off the stereotype of a lumbering footballer to offer an exhibition of the complete attacking midfielder. The goal he smacked beyond Lloris for United’s first came from a smart run and left-footed finish that demanded Fellaini should finally be taken seriously as a Manchester United player. To revive the career of a £27.5m apparent misfit is a big feather in the Van Gaal cap. To see the £37.1m Juan Mata snapping at Tottenham heels and barging the men in white aside while doing the balletic stuff that is his calling card is another. This was the Spaniard’s first league start for two months and Mata took his chance.

How the watching Ángel Di María and Radamel Falcao assess their hopes of breaking back into the starting XI would be interesting to learn. They were the two bona fide superstars who arrived last summer to usher in a new galáctico era. Yet neither was required as the two David Moyes signings, Fellaini and Mata, took their berths to be among the pivotal players in the victory. Di María is available for Sunday’s trip to Anfield having served his one-game suspension and Falcao is ready whenever selected.

But why change the side after this performance? The 4-1-4-1 (or 4-3-3 as Van Gaal calls it) sent out against Tottenham also featured a revitalised Ashley Young on the opposite flank to Mata, and Fellaini in a quasi-No10 role, so where the manager can fit in Di María or Falcao is a puzzle that may not be worth solving.

This was, though, only one outing so whether United can repeat it is the big question. Yet two defeats in 21 league games is stellar form. “If you look at 90 minutes, it is our best,” Daley Blind said. “In the last few weeks and months, we have been improving and we’ve played good halves before, but today we were really aggressive for almost 90 minutes. That’s a step [forward] for this team.

“Everybody was working hard together and fighting for each other, winning every ball we could. And we played like a team. It was really enjoyable to play.”

This had been the perfect response to being knocked out of the FA Cup by Arsenal in United’s previous outing. Blind added: “If you lose a game, you always want to play the next straight away. If it’s a cup game, it’s very disappointing, but if you lose in the Premier League, you want to win the next game.”

Second place would ultimately be an impressive achievement in Van Gaal’s debut Premier League season. Of the closing nine matches, Blind said: “You’re always looking up but the important thing is to watch yourselves, play your own games and try to get three points every game. They’re all finals now and we have to realise that.

“It was very important to get the three points – we have some difficult games coming up and we need all the points we can get. I think this was the start of something nice.”

This is the quest: to repeat the display of Sunday when Van Gaal moved from appearing the man-with-too-many-plans to a touchline Napoleon with the vision and imagination to make a brighter future at Old Trafford a reality.