David Moyes says West Ham's priority remains Premier League survival but has not ruled out a FA Cup run.
Pablo Zabaleta and Pablo Fornals came off the bench to down Gillingham after the Hammer toiled in the first half.
Moyes has two wins from two after returning as manager, following a 4-0 thumping of Bournemouth on New Year's Day, and was happy with his players grinding out the result.
"It was a real tough game, it wasn't easy," he said. "The players showed great character, they stuck together because we have lost this sort of game before.
"It's two games and two clean sheets. That builds up a bit of confidence and self-belief.
"We have to keep that going now and continue to be hard to beat but ultimately we want to score goals. We have scored six in the two games and hopefully that will continue."
West Ham have progressed to the fourth round for the third consecutive year - their best run for 13 years, but West Ham's Premier League status remains Moyes's main focus.
He continued: "If we can keep going in the cup, I want to do so, but the Premier League is always everyone's priority. I would love to be in the final and win a final, that's for sure."
