Two late goals underscored West Ham's second home victory in the space of five days and a 3-0 win over Derby that was less decisive than the scoreline suggests.
After leading by an early Joel Piroe goal, Nuno Espirito Santo's side lost their fluidity as the game progressed and were grateful to substitutes Edvin Austbo and Mohamadou Kante, each of whom scored their first goal for the club.
West Ham still looked ponderous at times as they adjust to the rhythm of the Sky Bet Championship, but they possess a quality that few sides in the division can match.
They took the lead after just six minutes with a goal of stunning simplicity.
Jarrod Bowen sent over a deep cross beyond the far post where Taty Castellanos headed the ball back across. It was dropping over the line anyway, but Piroe made sure by volleying home.
Unsurprisingly, Bowen looked the most likely source of a second West Ham goal. Time and again he received the ball just outside the Derby area and kept Charlie Taylor guessing which side he would attempt to jig past the full-back.
The England international dragged one shot wide and found the midriff of Derby goalkeeper Jacob Zetterstrom with two more efforts later in the first half.
Bowen's corner just after the half-hour was met powerfully by the head of Konstantinos Mavropanos who brought a superb reaction save from Zetterstrom.
Derby were forced to replace the injured Rhian Brewster with David Ozoh after 22 minutes.
The visitors rarely threatened the West Ham goal in the first half and were fortunate not to go in 2-0 down at the interval when Castellanos played a delightful one-two with Divine Mukasa before shooting inches wide of the far post.
Early in the second half impressive teenager Mukasa, back on loan with the Hammers after coming through the London club's academy until he joined Manchester City a year ago, again demonstrated his technique and vision.
The 19-year-old played a prominent part in a move that ended with Bowen testing Zetterstrom with a shot from the edge of the area.
Much of the energy that was on show in the midweek 4-2 win over Wolves was missing from Nuno's team as the game approached the hour.
The intensity of their pressing game dropped and their 1-0 lead started to look precarious as Derby began to believe that a point might be within their reach.
Had substitute Lars-Jorgen Salvesen not sent a free-kick inches wide in the 80th minute, the murmurs may have grown in volume.
Instead, Austbo, who signed for £10million from Norwegian club Viking on transfer deadline day, turned the ball home for a debut goal after Bowen had miscued his shot from an Arne Engels cross.
Any nerves were then completely dispelled when 20-year-old academy product Kante made it 3-0 with a rasping low shot from outside the area.
West Ham's Nuno Espirito Santo:
"It has been a very good, very positive week for us. Two good results and much-needed results. There were some good spells of football overall today.
"We didn't give them too many chances, which is really positive, and to achieve a clean sheet is always a boost of confidence for us.
"Of course we wanted to end the game sooner, but in the end I was so happy for the players who came off the bench, they brought energy and scored to help the team.
"We improved on our combinations today, but we still need to be better. It will take time. Once the players get to know each other better it will gel, so I am very positive.
"We have to repeat things again and again. The new players need their confidence. Let's see how long we can sustain our level of performance.
"It is a very tight schedule with the next game on Tuesday and then on Friday. But there are many things to be positive about.
"For the substitutes to score helps them get confidence more quickly. Of course, winning helps our legs to recover."
Derby's John Eustace:
"We started quite slowly and it's disappointing to concede such an easy goal in the first half. Against a quality team you cannot give them chances like that.
"But then we grew ourselves into the game a little bit, we adjusted a few things at half-time and after the break we really imposed ourselves onto the game.
"It was just in the final third that we lacked the quality or belief that we needed. We should have imposed ourselves and really believed in ourselves a little bit more, and we could have come away with something."
