José Mourinho warned about potential “roadworks” ahead for Manchester United but his players have navigated their way through the first two games of the season serenely enough, collecting maximum points, scoring freely and looking like a side who have all the credentials to mount a legitimate challenge for the Premier League title.

These are early days, of course, and United will certainly face much tougher examinations than those posed by West Ham United and Swansea City. Yet there is something ominous about the fact that they have started by racking up four goals in each of the opening two league games – the first time United have done that since 1907 – and also demonstrated that they have the ability to go through the gears as and when required.

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That shift came in the final 10 minutes here as United, with a devastating spell of attacking football, scored three goals in the space of 221 seconds to not just take the game away from Swansea but inflict a thumping defeat. Romelu Lukaku, who had been kept quiet for much of the game, registered his third United goal while Paul Pogba and Anthony Martial also scored for the second successive game.

It was, in short, a perfect away day for Mourinho, although the United manager is not getting carried away. When the statistics about the start of the 20th century were thrown at him afterwards he responded by pointing out that United won the first two games last season and ended up sixth. The key difference between that team and this one, according to Mourinho, is confidence.

The question Mourinho is interested to answer is how his team respond to going behind – something the United manager came close to discovering after only three minutes when Jordan Ayew hit the crossbar from an acute angle. That, however, was as close as Swansea came to scoring on an afternoon when their attacking limitations in the absence of the departed Gylfi Sigurdsson and the injured Fernando Llorente were once again laid bare. Swansea have failed to score in their first two matches of the season and registered only one shot on target – an overhead kick from Martin Olsson that was more of a cross and comfortably caught by David de Gea.

Paul Clement badly needs the Sigurdsson fee to be reinvested and fast. Swansea’s net spend this summer is the lowest in the Premier League and that has been reflected in their performances against Southampton and now United. “When you haven’t got Gylfi, Llorente, who is injured, and Ki Sung-yueng, who finished the season strongly, we’re weaker,” Swansea’s head coach said. “Texts, emails and telephone calls are going back and forth between various parties [with a view to making signings] because the necessity is there, it’s clear. We need to do some good business.”

Facebook Twitter Pinterest Eric Bailly opens the scoring for Manchester United just before half-time. Photograph: Dimitris Legakis/EPA

Despite the emphatic nature of the scoreline, this had actually started as one of those days when United needed to be patient as Swansea, playing with a five-man defence, sat deep. The visitors got a little frustrated at times. Marcus Rashford showed flashes of brilliance but also moments of petulance and Pogba was involved in that incident with Olsson not long after being booked for a foul on Tom Carroll. It felt like one of those challenges that would almost certainly have led to a yellow card had Pogba not already been booked.

The breakthrough arrived for United on the stroke of half-time. Daley Blind’s corner exposed some poor marking in the Swansea defence, leaving Pogba with a free header. The Frenchman’s effort was flicked on to the bar via Lukasz Fabianski’s fingertips, bounced on the line and Eric Bailly, reacting much quicker than Federico Fernández, who seemed to be expecting the Swansea keeper to jump to his feet, stabbed home. It was Bailly’s first league goal in 67 appearances for three different clubs.

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Clement felt the need to make a couple of attacking changes early in the second half – “I don’t want to be a coach that’s happy to lose 1-0 at home,” –but Swansea never seriously threatened to equalise and the game was in effect over for them when Lukaku, set up by Henrikh Mkhitaryan and in so much space, swept a left-footed shot past Fabianski.

After that Swansea capitulated. Carroll’s wayward pass was intercepted by Pogba, who played a one-two with Mkhitaryan, continued his run and deftly lifted the ball over the advancing Fabianski. In the blink of an eye it was 4-0 as Martial, teed up by Pogba, calmly slotted in the fourth. “The second goal was a gift,” Clement said. “And then we played into their strengths, 2-0 down, trying to get a goal back, a loose pass, you get hit on the counterattack and then another counterattack, 4-0. It’s a hard one to take in the end.”