Substitute Jay Rodriguez scored an 89th minute winner, heading past Aaron Ramsdale from Ashley Westwood's cross to send the Clarets 10th in the Premier League. Here's how we scored the players on the South Coast.
1. Nick Pope 6
A second game in succession where the opposition failed to register a shot on target, but did the basics well. Handling was good, though the conditions caused a few issues with his kicking.
2. Phil Bardsley 6
His physicality helped break up the play on a number of occasions and kept fellow Scot Ryan Fraser quiet throughout.
3. James Tarkowski 7
The centre half won't be far away from Gareth Southgate's Euro 2020 squad should he continue in this run of form. He was a rock at the heart of Burnley's defence.
4. Ben Mee 6
Protected Nick Pope's goal heroically once again, keeping the home side's chances in the final third at a premium. Won everything that came his way.