The last time that Chelsea enjoyed themselves like this was on 22 December in what felt like the statement result of Frank Lampard’s tenure. It was the 2-0 victory at Tottenham, which finished with the manager slinging his coat into the travelling enclosure and joy bursting from every pore.

This was another comprehensive triumph over the team that Chelsea most love to hate and Lampard showed what it meant with another round of lusty post-match celebrations. After a sticky run of form, he needed this, Chelsea needed this, and it was a result to reinforce their grip on fourth place in the Premier League.

Do not be fooled by the scoreline. Lampard’s team might have been 3-0 up before Antonio Rüdiger turned an 89th-minute cross from the Spurs substitute Érik Lamela into his own net and that was a rare sortie from the visitors into the final third.

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Spurs might have lost Giovani Lo Celso to a 52nd-minute red card after a stamp on César Azpilicueta. It was a spiteful challenge, albeit one that looked worse on the slow-motion replays, but both the on-pitch referee, Michael Oliver, and the VAR, David Coote, decided that it did not merit a dismissal. Coote would later change his mind on this but there can be no in-game review of the VAR.

It was the only time José Mourinho and Spurs caught a break. Chelsea’s win was not in doubt from the moment that Marcos Alonso made it 2-0 with a firecracker from distance early in the second half, building on the lead given to his team by Olivier Giroud, and they had the chances to turn the screw. The substitute Tammy Abraham was denied by a reflex save by Hugo Lloris while Alonso rattled the crossbar from a free-kick.

Spurs could get precious little going and, listening to Mourinho afterwards, it was no surprise. He had dropped Dele Alli and started with an ultra-defensive 5-4-1 formation but, with injuries biting – particularly to Harry Kane and Son Heung-min – he indicated that his hands were tied. He said that he was forced to use players out of position, such as Steven Bergwijn at centre-forward, and try to hang on and hope; in effect to pray for “miracles”. Mourinho is rarely slow to chronicle his difficulties but it was still surprising to hear him say that he wanted the season to end.

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“I would love to be at 1 July,” Mourinho said. “I would love to be in pre-season, working with Harry Kane, Sonny and [Moussa] Sissoko [another injury casualty]. That’s not possible. And we have three long months to go in three competitions. These boys will learn a lot from that. So I think a very difficult experience for the boys but a very good experience for the future.”

Mourinho said that Spurs needed to score the first goal and they nearly did when Bergwijn teed up Lucas Moura and he shot low for the corner. Willy Caballero made a smart save.

But it was Chelsea who played on the front foot, probing with quick passes up the channels, with Lloris denying Mason Mount after one from Alonso. The breakthrough goal originated from a similar ball from Jorginho, fizzed up towards Giroud, who saw his first shot saved by Lloris. After Ross Barkley hit a post from the rebound, Giroud took a fine touch and lashed the ball low inside the near post.

It was Giroud’s first start since 30 November and how he took his opportunity, not just with the goal, which was his first of the season, but his all-round link-up play.

Alonso, too – another player recalled to the lineup by Lampard – more than justified his manager’s faith. The left wing-back had narrowly missed the top corner with a blast from distance midway through the first half but everything came together for him on 48 minutes.

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What a strike it was, a celebration of technique, cutting across a pass from Barkley, which produced the sweetest of connections to send the ball hurtling into the far corner. Giroud had started the move, flicking on to Mount, and the midfielder drove forward before squaring for Barkley.

Spurs had flickered briefly towards the end of the first half, with Moura seeing a shot blocked by Azpilicueta and Davinson Sánchez extending Caballero with a header from a corner. There was also the moment when Japhet Tanganga got in behind Alonso following Toby Alderweireld’s precision long ball only to take a heavy touch. Caballero had left his line and lost his bearings and he was relieved to see Tanganga’s touch take the ball all the way past the far post.

Mourinho asked his players to take higher starting positions in the second half and Tanguy Ndombele almost danced through, beating two Chelsea players but not a third in Reece James. It was an isolated flicker. Chelsea could point to a Barkley effort on 50 minutes that worked Lloris and, despite the late scare, they could close out the result with comfort.