West Ham manager Slaven Bilic felt a sense of "relief" after Diafra Sakho's late goal secured victory over Swansea and eased the pressure on him.
The atmosphere at London Stadium had been tense with fans unhappy about the performance of Bilic's side for the majority of the game.
But Sakho eased some of the scrutiny on Bilic when he got on the end of fellow substitute Arthur Masuaku's cross in the 90th minute and stabbed the ball home from close range.
"It is a relief, a great three points for us," Bilic said. "I know it is shallow when the manager says there is pressure, but that makes a difference.
"To keep the support of the crowd we need to keep producing minute after minute and we did not do that in the first half. The guys on the bench lifted the team and crowd."
Swansea were positive with their approach but a long-range effort from Wilfried Bony, parried by Joe Hart, in the first half was the best they had to show for their endeavour.
Home fans chanted "sacked in the morning" at Bilic when his side trailed 3-0 in a 3-2 defeat by Tottenham last weekend.
For the most of this contest there was little respite for the Croat as his side laboured against a disciplined and organised Swansea side.
Indeed there were jeers and boos for Bilic's double substitution when Masuaku and Sakho were introduced for Javier Hernandez and Andre Ayew.
Ultimately, the 49-year-old's decision to throw on both players made the difference, though, as Masuaku's superb run and cross found Sakho's perfectly timed run.
With West Ham's next three matches against Burnley, Brighton and Crystal Palace, Bilic will hope the confidence from this victory can spur his side on to greater things.
Swansea managed just 10 shots on target before this encounter, which head coach Paul Clement blamed on a hectic end to the transfer window.
Their play was largely tidy and they used the ball intelligently, with Renato Sanches in particular catching the eye for the visitors.
However, there was a stark lack of cutting edge to Swansea's play. Despite the presence of Tammy Abraham, Jordan Ayew and Bony - for the first half at least - they managed just one shot on target in the entire contest.
"A combination of the delivery and the movement need to be better in the final third," Clement said. "We are closer to getting the balance right, but there is still work to be done."
Swansea's first away defeat sent them into the bottom three and, unless Clement gives them more bite in attack, another relegation battle beckons this season.
The powerful striker's partnership with Javier Hernandez never really clicked but he was a menace to the Swansea backline. Carroll seems to be getting sharper and his all-round workrate was unrelenting. He was unfortunate not to score when he struck the corner of the goal with an improvised shot.
This game produced a total of just 15 shots; only Burnley v Huddersfield on 23 September featured fewer in the top flight this season (13).
West Ham have registered three clean sheets in their last four Premier League games, after managing none in the five before that.
Swansea conceded their first away Premier League goal in 495 minutes of action and suffered their first away defeat of the season.
Four of the 10 Premier League games where winning goals have been scored in the 90th minute or later in 2017 so far have been against Swansea.
Diafra Sakho netted his first Premier League goal since November 2016, when he scored against Manchester United.
Six of West Ham's seven league goals this season have come in the second half, which equates to a league-high 86% proportion.
West Ham goalkeeper Joe Hart: "It was a difficult atmosphere in some ways. I'm never going to criticise the fans, they come here and pay their money and have a right to their opinion.
"We have to focus on the win. We have had seven points since the international break [at the beginning of September].
"It is on all of us to take the pressure off. We don't get sucked into the speculation, we just stick together and fight hard."
Swansea head coach Paul Clement: "I think the result was a little harsh in that I don't think that they weren't better than us as such.
"We just did not defend that last attack very well. They created a really good scoring chance, which is what we didn't do.
"We did not stop the cross coming in, did not defend it in the box and if you concede that late you do not give yourself much chance."
West Ham manager Slaven Bilic: ""We did not play well in the first half after a good first 10 minutes, making basic mistakes and Swansea were much better on the ball. We have to play better and we can play better.
"The changes were crucial with Manuel Lanzini, Arthur Masuaku and Diafra Sakho coming on.
"We played a very offensive formation in the first half but lacked the link between the defence and attack and that was why Lanzini made a big impact."
West Ham face a tricky trip to Burnley on Saturday, 14 October (15:00 BST), while Swansea host newly promoted Huddersfield at the Liberty Stadium at the same time on the same day.
Match ends, West Ham United 1, Swansea City 0.
Second Half ends, West Ham United 1, Swansea City 0.
Attempt blocked. Andy Carroll (West Ham United) left footed shot from the left side of the box is blocked. Assisted by Diafra Sakho with a cross.
Goal! West Ham United 1, Swansea City 0. Diafra Sakho (West Ham United) right footed shot from the right side of the six yard box to the high centre of the goal. Assisted by Arthur Masuaku with a cross.
Attempt missed. Andy Carroll (West Ham United) left footed shot from outside the box misses to the right. Assisted by José Fonte following a set piece situation.
Substitution, Swansea City. Sam Clucas replaces Martin Olsson.
Andy Carroll (West Ham United) hits the bar with a left footed shot from the centre of the box. Assisted by Arthur Masuaku with a cross.
Offside, West Ham United. Michail Antonio tries a through ball, but Diafra Sakho is caught offside.
Alfie Mawson (Swansea City) wins a free kick in the defensive half.
Substitution, West Ham United. Arthur Masuaku replaces André Ayew.
Attempt missed. Martin Olsson (Swansea City) right footed shot from outside the box misses to the right. Assisted by Leroy Fer.
Renato Sanches (Swansea City) wins a free kick in the defensive half.
Substitution, Swansea City. Roque Mesa replaces Leon Britton because of an injury.
Delay in match Lukasz Fabianski (Swansea City) because of an injury.
Substitution, West Ham United. Manuel Lanzini replaces Mark Noble.
Attempt missed. Renato Sanches (Swansea City) right footed shot from outside the box is too high from a direct free kick.
Renato Sanches (Swansea City) wins a free kick on the right wing.