Moyes was appointed for a second spell in charge following the departure of Manuel Pellegrini on December 28 and oversaw a 4-0 win over Bournemouth in his first game in charge on New Year's Day.
A potential banana skin in the FA Cup followed on Sunday as the Hammers travelled to League One Gillingham in the third round.
With the surface uneven and the Gills not letting the visitors settle at the Priestfield Stadium, the pair went in 0-0 at the break.
West Ham eventually broke the deadlock on 74 minutes through an unlikely source in Pablo Zabaleta, before fellow substitute Pablo Fornals added some extra gloss in stoppage time to seal a 2-0 win.
Moyes experimented with a three-man defence to try and counter the physical threat possessed by Gillingham and his team defended well.
However, he had some reservations about the tactic, admitting his wing-backs were not aggressive enough.
Even so, having needed five games to claim his first win when he previously took charge in 2017, the Scot has a perfect record from his two games second time around.
Next up for the Hammers is a trip to Sheffield United on Friday and rather than resting on his laurels after two wins from as many games, the 56-year-old says his team still need work.
"We got a deserved win in the end, but it was a really, really tough game," he is quoted as saying by the club website.
"There is lots of room for improvement, but the good thing was the resilience and character of the players."
West Ham sit 16th in the Premier League table and also face Moyes' former club Everton, Leicester and Liverpool before the end of the month, as well their prospective opponents in the fourth round of the FA Cup.