After netting the only goal to keep alive his side's outside chances of keeping in touch with pacesetters Manchester United, Anelka believes today's win shows the character in the side.
He told Sky Sports 1: "We showed it last week and again, today, we showed a lot of character because it was a hard game.
"It is good for all the players and for the new coach as well because we can continue this winning way and we hope we can win more games.
"It is going to be difficult but we think it is possible. We hope we are back in the race."
Hiddink was encouraged by the start to his temporary tenure. "It's a very good start in new circumstances and a new situation," he said.
"What pleased me most was the first half, we played very good football, had good possession and were dangerous.
"The only thing we didn't do was score a second to kill the game."
"It is important - if you see Villa's home record, it's good we could break that."
The Chelsea players came together in a show of solidarity after the full-time whistle - perhaps responding to suggestions there are cliques within the squad - although Hiddink played down the significance.
He told Sky Sports 1: "I'm analysing it but I didn't see what has sometimes been described as a big division.
"When they hugged each other afterwards, I don't think it was showing off for the camera. I think it's real."