After a disastrous start to the season, which saw them lose their first seven games without scoring, Hodgson's side are now unbeaten in their last seven - a club-record run in the Premier League era.
"Before the game I was asked about our away form, and I think I said the last performances in particular we've looked very dangerous and just haven't quite taken all of our chances," Hodgson told Sky Sports News after the game. "But today it all fell for us, we were solid defensively and the two forwards did very well up top. I'm delighted with the result, but I'm not that surprised by it either, because we've been playing very well for a while now.
"They were all excellent. I wouldn't criticise any aspect of our performance today, and that's our third clean sheet in a row away from home. We've moved away from that situation we were in after seven games - we were in a bleak situation - but since then we've shown we can get points and we've re-established some parity with the rest of the teams around us."
Palace's festive schedule sees them travel to rock-bottom Swansea City next Saturday, ahead of tough back-to-back home encounters with Manchester City and Arsenal.