Nunez’s goal was his fourth for Liverpool but his first at Anfield following his off-season move from Benfica.
The goal came amid an industrious display where he also struck the woodwork with a powerful effort.
Given Liverpool’s early season struggles, Nunez’s three-game suspension for a headbutt against Fulham wasnt timely, ensuring he didnt endear himself to the Reds’ fans but Klopp said he is winning them over now.
“It is important. He has scored now a couple of times in the last few games,” Klopp said. “He arrived 100 per cent, now even with numbers, which is fine.”
The win, coming days after Liverpool upset Manchester City 1-0, was hard fought with West Ham blowing late chances from Gianluca Scamacca and Tomas Soucek, the latter blocked by James Milner’s desperate challenge.
Liverpool also had goalkeeper Alisson Becker to thank, saving Jarrod Bowen’s 45th-minute spotkick after a reckless Joe Gomez tackle.
“I think the first half was a really good first half, with a bad ending for us with the penalty… but then with a good ending because Ali could save the penalty,” Klopp said.
“It still left a bit of a bad taste like we were lucky, but first half we were not - we played an exceptional game.
“If you don’t control it, West Ham are there, then the long balls flying in and great set-pieces. In the end, we needed Ali, we needed Millies big toe and we needed a couple of things.
“Overall, I think it is a deserved three points. It is a very important, tough period for all teams so you have to grind results out and now in three days time the next fight is waiting already.”
Miguel Almiron struck the winner on the half hour as Newcastle edged Everton 1-0, while Manchester United defeated Tottenham 2-0.