Lazio won at San Siro on Sunday. An impressive feat at any time but all the more so on this occasion because they weren’t playing there. It was their neighbours, Roma, who had travelled to face Inter but a 1-1 draw between those teams was as good as a victory for the Biancocelesti, who took advantage of dropped points to climb into joint third.

They had done their part by thrashing Chievo 5-1 in the afternoon. So much for the theory that the winter break might cost Lazio momentum. This was the fourth time in 20 games they had hit five or more goals in a match – including a 5-2 win over Spal immediately before Serie A’s one-weekend pause.

Remarkable stuff, especially when you consider they lost Serie A’s leading scorer to injury on Sunday after only 35 minutes. Ciro Immobile should have exited much sooner – tweaking his thigh soon after kick-off and making little impact on the game thereafter. Instead it was Luis Alberto who opened the scoring with a deflected effort, and then Sergej Milinkovic-Savic who restored Lazio’s advantage after Manuel Pucciarelli had equalised in between. The Serbian added an elegant volleyed finish midway through the second half before Bastos and Nani completed the rout of Chievo.

You could argue the final scoreline was misleading. Chievo were competitive for long stretches and things might have gone differently if the penalty they were awarded with the score 2-1 had not been overturned on a VAR review. Yet there is something compelling about the way this Lazio side finishes games – refusing to let up even after an opponent’s will has been broken.

Their 53 goals are the most of any team in Serie A, despite the fact they have a game in hand on the majority. They have got there by a different route to the other frontrunners, too, eschewing possession in favour of fast breaks and faster finishing: a ruthlessly efficient brand of counterattacking football devised by manager, Simone Inzaghi.

It’s a system that exploits the talent at his disposal. Immobile divides opinion, a centre-forward who lacks the all-around game of the world’s best at his position and who struggled badly when called upon to become a more complete player at Dortmund and Sevilla. Yet his instincts and timing around the 18-yard box are exceptional. Limit his role to what he does well, and he can be very effective indeed.

Likewise, Milinkovic-Savic and Luis Alberto have flourished in roles behind the attack, empowered to carry the ball forward and assault spaces that open up when an opponent overcommits. With Immobile running on ahead of them, defenders are routinely confronted with the stark choice of backing off and inviting one of those two to take a shot on themselves, or risking the ball in behind.

Inzaghi has, in short order, emerged as one of the most promising young managers on the peninsula – a fact that only looks more impressive when you consider he is going against current tactical trends. Not bad for a man who was initially only intended as a caretaker appointment in the spring of 2016 and who got the job full-time only because Marcelo Bielsa changed his mind about taking it in the summer.

Nani scores against Chievo. Photograph: IPA/Rex/Shutterstock

Perhaps Lazio could have avoided that whole saga if they had listened to the players. “As soon as [Inzaghi] arrived, he just brought this positive energy that made us feel right,” Milinkovic-Savic said during a June interview with Serbian media. “He created this atmosphere in which everyone trusts their team-mates. There are no cliques – where I might, say, only speak to [compatriots] Dusan Basta or Filip Djordjevic.”

To focus solely on the manager, though, feels reductive. Lazio owe their success also to the recruitment strategy that brought in such players as Milinkovic-Savic – these days a reported €100m target for Europe’s wealthiest clubs – for barely a tenth of that sum in 2015.

The sporting director, Igli Tare, has consistently found value in the transfer market, be it precocious young talent or players in need of a reboot – from Immobile to Luis Alberto and Lucas Leiva. All this while allowing supposed pillars of the team to move on, without adverse effect. This team has not missed Lucas Biglia, Antonio Candreva or Keita Baldé.

Indeed, what stood out on Sunday was how well-equipped Lazio were to handle Immobile’s injury. Felipe Anderson, still working his way back into form after missing the start of the season, was sent on to replace him as a false nine. Although not accustomed to the role, the Brazilian’s pace is well-suited to the task of dragging defenders out of position, leaving that space for Milinkovic-Savic and Luis Alberto to exploit.

And then there is Nani, a bit-part player so far but capable of chipping in both a goal and an assist in his 15 minutes on the pitch. Improbably, for a team competing with more modest financial resources than Inter or Roma, Lazio might boast better depth than either.

With a busy January window in prospect, that situation might yet change. But for now, Lazio can look forward to a home game against Udinese on Wednesday, and an opportunity to pull clear in third. Where Roma and Inter have each seen their form dip catastrophically since the start of December, Lazio have won three of their last four. And that’s not even counting the one they got in absentia at San Siro on Sunday.

Talking points

• Dries Mertens sent a message to his fantasy owners last week, an Instagram picture of himself laughing on a beach and a reassurance that “I’ve rested up nicely”. On Sunday, he delivered them a goal – his first in the league since October. It was a lovely strike (possibly offside) and even more timely for his real team, since it earned Napoli a win at Atalanta. The Partenopei had lost three of their last four games to these opponents, who have taken points off both Lazio and Juventus in Bergamo. This season still has a mighty long way to run, but these are the sorts of wins that make the Scudetto dream start to feel very real indeed.

A big win for Napoli. Photograph: Marco Bertorello/AFP/Getty Images

• Of course, the real fantasy football winners this season are those who bet on Fabio Quagliarella. The Sampdoria striker grabbed a hat-trick in a 3-1 win over Fiorentina , moving to 15 goals on the season. That is his personal best in a league campaign – with 18 games to play.

• What a season Alisson is having for Roma. Beyond a string of vital saves that oh-so-nearly earned his team the win at San Siro, he also provided the assist for Roma’s goal and seemed to spend about half the game eluding forwards and distributing calm passes from the edge of his box.

• By contrast, should there be anxiety in Milan regarding the form of Gianluigi Donnarumma? He misjudged the flight of the ball badly as the Rossoneri fell behind at Cagliari, though they would recover to win 2-1. According to whoscored.com, he has made more errors leading to opposition goals than any other Serie A player this season.