An out of sorts Liverpool dominated possession, but struggled to break the well organised hosts down in the first half, before Sadio Mane missed two glorious chances for the league leaders.
First slicing high and wide when clean through before hitting the post from close range, as it remained goalless at the break.
Oliver Norwood forced Adrian into a fine save in the bottom right hand corner before a double block denied United after flooding forward on the break.
A mistake from Henderson gifted Wijnaldum and Liverpool the opener. The United keeper not fully behind the midfielder’s volley as it squirmed through him and just over the line.
Mo Salah should have put the result beyond doubt with just over ten minutes to play, but Henderson made up for his earlier mistake, denying the Liverpool talisman with his leg when one-on-one.
That save would have been all the more important if substitute Leon Clarke managed to hit the target from six-yards out, but he blasted over from a superb cross from the left.
The win sees Liverpool move eight points clear of Manchester City at the top with seven wins from seven.
It was harsh result for United who, despite their Premier League inexperience, had given Liverpool as tough a test as anyone this season.
Their well-drilled 5-3-2 formation gave the visitors more problems than they would care to admit considering the attacking talent they had at their disposal with their build-up play laboured and lethargic.
And with Oli McBurnie a danger on the counter-attack down the left there was even the threat of even more trouble with the striker testing Adrian early on, before Callum Robinson fired a shot wide after being put through by John Fleck.
The direct approach proved more profitable for Liverpool as Virgil Van Dijk lofted a pass for Mane to run clear of the defence but he sliced high and wide with only goalkeeper Henderson to beat.
Mane should have done better with that effort but the one two minutes before the break was even more inexplicable.
Wijnaldum launched Salah on the counter-attack which resulted in Firmino, seven yards out, opting to tee up Mane but although his shot beat Henderson at his near post the upright denied him the opener.
Jurgen Klopp changed tack 20 minutes into the second half, sending on the fit-again Divock Origi for Jordan Henderson and switching to a 4-2-3-1 formation with Salah as its spearhead.
The best chances were still falling to the hosts, however, with Norwood forcing to tip a low drive around the same post Mane had struck until Liverpool benefited from a huge stroke of luck.
Just when it seemed United were about to become only the only side after Barcelona and Napoli in the last 26 games to prevent the Reds scoring, Henderson gifted the Reds the lead.
Wijnaldum's shot from the edge of the area was hit well but more in hope than expectation but, as it flew through a crowd of players, United's goalkeeper failed to get a proper hold and it slipped between his hands and then his legs to trickle over the line.
Henderson's sticking out a leg to deny Salah clean through one-on-one prevented it becoming 2-0 but the damage had been done.
Nevertheless, substitute Leon Clarke should have equalised five minutes from time but ballooned over Fleck's low cross from close range.
Liverpool's perfect start to the season continues with their 16th Premier League win in a row.
Additional from PA.
Featured from our writers