Niko Kalinic broke the deadlock shortly before half-time and second-half strikes from substitute Jason Roberts and defender Gael Givet secured the points.
Allardyce said: "It was a fantastic day for us and a very important three points.
"It's our biggest win of the season and four wins on the trot at Ewood Park. We're making everyone sit up and think what a game they're going to get here - and they certainly are."
But Junior Hoilett and Steven Nzonzi could have extended the lead before Roberts' scruffy goal, after which point Allardyce could relax once more.
"It was a difficult game," he admitted. "One; because of the weather, and two; it's a local derby.
"But we deserved a 1-0 lead in the first half. We then sat back on that a little too much and Bolton had their best spell and threatened that they might get something.
"But when the best chance of the game for them came we've got Paul Robinson, who made a match-winning save.
"Then we got the biggest snowflakes you've ever seen in your life - I was struggling to see the ball and the players almost, they were that big!
"Once we'd weathered that storm we had Junior Hoilett, with a diving header that Jussi (Jaaskelainen) saved, and Steven Nzonzi with the header, and I was wondering if and when the second goal was going to come.
"But when we got that it knocked the stuffing out of Bolton and we just opened them up if and when we saw fit. The third goal went in and it could have been four in the end, perhaps five."