Revell's double earned Brighton their first home victory in League One since September and moved them to within four points of their Welsh victims, who remain in the play-off zone.
Brighton dominated the first-half and were good value for a 13th minute lead provided by Dean Cox.
The diminutive left winger scored his eighth goal of the season with a swerving shot from 30 yards.
Cox ran the show for Brighton in the opening 45 minutes but Swansea still could have been level at the break after a cross by the towering Dennis Lawrence was met with a looping header on to the top of the bar by Adebayo Akinfenwa.
That seemed to spur Swansea on and they were level in the 59th minute when the tall defender headed in a cross from Andy Robinson.
Swansea looked the likelier winners at that stage but they were reckoning without Revell.
The former Braintree forward restored Brighton's lead in the 66th minute, diving to bravely head in a free-kick from Sam Rents.
Revell made it 3-1 just 14 minutes later, blasting home at the second attempt after Dean Hammond's header from a Kerry Mayo corner had been blocked on the line.
Swansea were still not finished despite having captain Darren Pratley sent off in the 84th minute for a second bookable offence.
Half-time substitute Rory Fallon reduced the arrears in the first minute of stoppage time when he slotted in from a tight angle following a mistake by Adam Hinshelwood.
Fallon should have salvaged a point for Swansea in the fourth and final minute of time added on but he fired over after Brighton keeper Wayne Henderson dropped a free-kick from Alan Tate.