At the Amex Stadium, Brighton broke a three-game goal drought when they took the lead through Pascal Gross's 14th minute penalty.
Ezgjan Alioski was penalised for bringing down Danny Welbeck and Gross found the bottom corner with the resulting spot-kick.
Graham Potter's side struck again through Danny Welbeck's excellent solo effort in the 79th minute to seal a 2-0 win.
Brighton are now 10 points clear of the relegation zone with four games left.
Later on Saturday, Chelsea can cement their hold on fourth place and push Fulham closer to relegation with a win in the west London derby at Stamford Bridge. Everton, pushing for European qualification, host Aston Villa in Saturday's final match.