Lukaku had netted in his first league appearances for both West Brom and Everton and he repeated that feat on Sunday, getting on the end of a Marcus Rashford pass to give the hosts a deserved lead in the 33rd minute.
Nemanja Matic also began to swiftly justify the fee paid by United to reunite the Serbian with his former Chelsea manager Jose Mourinho, impressing throughout at the base of midfield and completing a timely interception to trigger the counter-attack that ended in Lukaku’s first goal.
The Belgian centre-forward doubled his tally eight minutes into the second half, when he headed home a Henrikh Mkhitaryan free-kick.
Substitute Anthony Martial and midfielder Pogba added gloss to the scoreline by scoring late on, leaving Mourinho and the home faithful cheered by the sight of a dominant display to open the campaign as they seek to challenge for a first league title since 2012-13.
A sustained run of away fixtures to open the campaign for West Ham, a consequence of London Stadium temporarily reverting to its original purpose to host the IAAF World Championships, continues with a trip to Southampton next weekend, when United are also on the road at Swansea City.
Mourinho watched his team dominate possession but struggle to create clear-cut opportunities in the first half, with former Manchester City goalkeeper Joe Hart, making his first Premier League start for West Ham, required to deny Juan Mata in the 18th minute. The Spaniard still managed to cut the ball back to the six-yard box, where Angelo Ogbonna prevented Lukaku from getting a shot away.
The best chance yet arrived in the 27th minute when Pogba’s lofted pass forward released Mata into a dangerous position inside the area. The ex-Chelsea and Valencia man could have taken a shot at goal but opted instead to try and square for Lukaku, Ogbonna again completing a good clearance.
There was no denying the Belgium striker six minutes later, though. A Matic interception just inside the United half allowed Rashford to break at pace, the youngster’s carefully weighted pass slipping in Lukaku to race in on goal and slam a fierce, first-time finish past Hart and into the back of the net with the help of the post.
West Ham had to wait until first-half injury time to register a shot on target, Edimilson Fernandes shooting straight at David de Gea in a frustrating conclusion to a flowing move involving Andre Ayew and Mark Noble.
They did not threaten again before United made it 2-0, the powerful Lukaku holding off Arthur Masuaku with ease to nod Mkhitaryan’s set-piece delivery into the bottom corner of the net, beyond the reach of a helpless Hart, as the Armenia international supplied his first league assist since February.
Lukaku narrowly missed out on a hat-trick just past the hour mark, Pablo Zabaleta, another former City man making his first competitive start for West Ham, required to pull off a desperate block following good work from Rashford down the left and Mkhitaryan’s lay-off.
Rashford hit the post with a rasping strike in the 66th minute as United’s sustained pressure continued, Daley Blind firing a volley down into the ground and just over the bar with 21 minutes to go.
A third appeared inevitable and it arrived when Mkhitaryan slipped Martial in to score in the 87th minute as West Ham fell apart late on.
And Pogba then struck from long range in injury time, perhaps serving notice of his intention to impress after struggling at times to convince in his first season back at Old Trafford last term.