Brighton took the lead in the first half when skipper Lewis Dunk powered home a header from Pascal Gross' pinpoint corner.
Burnley however were always a threat going forward and their pressure told after the break when Johann Gudmundsson blasted home from 15 yards.
Brighton showed plenty of spirit and worked hard for their point after their energy sapping victory at champions Liverpool last Wednesday.
Graham Potter's team were also thankful to their keeper Robert Sanchez who produced numerous good saves throughout.
Brighton remain unbeaten in the Premier League in their last five matches.
Scroll down and click through to see how they rated.
.
Skipper Lewis Dunk rises high to open the scoring for Brighton
. Robert Sanchez 8/10
Brave stop from the Spaniard on 27 minutes. Scooped Tarkowski's shot away and also a strong one handed save on 45 minutes. Numerous saves in the second half and unfortunate with the goal after his initial save
. Ben White 7/10
Another solid display in what was a physical encounter. One very timely tackle in the penalty areas to deny Ashley Barnes a certain goal. Started on the right of a three, moved into central midfield and then ended at centre back
1. Robert Sanchez 8/10
Brave stop from the Spaniard on 27 minutes. Scooped Tarkowski's shot away and also a strong one handed save on 45 minutes. Numerous saves in the second half and unfortunate with the goal after his initial save
2. Ben White 7/10
Another solid display in what was a physical encounter. One very timely tackle in the penalty areas to deny Ashley Barnes a certain goal. Started on the right of a three, moved into central midfield and then ended at centre back
3. Lewis Dunk 7/10
Fantastic header for the opening goal. Had a few defensive problems with Vydra early on but stood up well to the Burnley pressure
4. Adam Webster 7/10
Blocked and tackled with everything he had. Always alert and has been an immense figure during Brighton's recent fine run. Forced off on 70 minutes with what looked like a knee injury and will no be keen to get a few days off