Bordeaux, who were unbeaten in their first nine league matches, threatened a comeback in the first half but the Corsican side had more in the tank after the break.
Bordeaux lie eighth in the standings on 15 points, seven behind leaders Paris St Germain who beat Nancy 1-0 away on Saturday.
Bastia are 11th on 14 points.
Thauvin put the hosts ahead after just six minutes when he fired home from close range after benefiting from some terrible defending.
Thauvin made it 2-0 11 minutes later, poking the ball home after Cedric Carrasso deflected a Toifilou Maoulida cross into his path.
Yoan Gouffran pulled one back for the visitors on the half hour mark. His volley was parried away by Novaes, but the midfielder followed up to slot home with his second attempt.
Wahbi Khazri curled a free kick into the top corner to make it 3-1 in the 56th minute.
The clash between third-placed Marseille and fourth-placed Lyon was postponed because of strong winds.
Earlier, Lorient avoided their second consecutive defeat when Gilles Sunu's last-gap goal salvaged a 4-4 comeback draw at home against AC Ajaccio.
Lorient were 4-1 down at halftime after Chahir Belghazouani, Adrian Mutu and Eduardo's double had put the visitors firmly in command.
The home side, who had been thrashed 6-1 at Valenciennes last weekend, reduced the arrears thanks to Jeremie Aliadiere's double and snatched a point when Sunu volleyed home four minutes into stoppage time.
Lorient lie ninth on 15 points while Ajaccio are 14th four points further adrift.