The Baggies were impressive from the start and took full advantage of a 10-man Chelsea team after Thiago Silva was sent off in the first half.
And Allardyce believes victory was thoroughly deserved, ten men or not, and praised his side for playing so positively.
“I think that we are really pleased and satisfied about how the players applied our tactics,” Allardyce told BT Sport.
“I have to say that, because the way we ended up being so good in possession was the best it’s been since I’ve been here, that it was a thoroughly deserved victory.
“People will talk about ten men but I’ve been in charge against men teams with ten men who have won. We took full advantage of that and started the game brightly.”
West Brom remain seventh points off satey in 19th place, and while Allardyce still believes five wins from their next eight games will be necessary to stay in the Premier League, he was happy to get three points today and gain some momentum.
“There’s a long way to go. But we’ve started on the track of trying to get an undefeated run,” he added. “We are trying to get more wins in the last eight games than all season. It’s been done before, and this is a good start.”
