The home side almost took the lead while the fans were still coming through the doors when Danny Whitaker's saved shot fell to the feet of Akpo Sodje but the striker rushed his effort and sent it wide.
A mistake by George Abbey almost proved disastrous for Vale when Alex Revell gained possession and fed Jake Robinson but the flag went up for offside.
Constantine equalled Vale's record for goals before Christmas in the 13th minute when an awful clearance by Adam Hinshelwood across the face of goal fell into the striker's path for an easy finish.
The Valiants were handed an early Christmas present by referee Phil Crossley ten minutes later when he awarded a dubious penalty against Richard Carpenter for handling inside the box.
Top-scorer Constantine stepped up and confidently struck the ball into the net, sending goalkeeper Wayne Henderson the wrong way.
Brighton almost pulled a goal back before the break when Andy Whing's long ball from the right eventually dropped for Tommy Fraser whose neat shot beat Mark Goodlad but not his right post.
Henderson was caught on the back foot in the 55th minute when a failed clearance fell straight to the feet of Constantine, but the in-form player was too patient with his shot and allowed the goalkeeper to recover.
The visitors finally created a threatening opportunity in the 66th minute when Alistair John cut inside from the right and struck a powerful shot from 20 yards that Goodlad saved with an outstretched leg.
Sodje's tireless running was almost rewarded with a goal when he hammered a 25-yard firecracker towards goal but the ball flew inches wide of Henderson's left post.
The Seagulls pulled one back in the 84th minute when after Colin Miles headed the ball against his own crossbar, Fraser pounced on the rebound to stab past a helpless Goodlad.
A mistake by George Abbey almost proved disastrous for Vale when Alex Revell gained possession and fed Jake Robinson but the flag went up for offside.
Constantine equalled Vale's record for goals before Christmas in the 13th minute when an awful clearance by Adam Hinshelwood across the face of goal fell into the striker's path for an easy finish.
The Valiants were handed an early Christmas present by referee Phil Crossley ten minutes later when he awarded a dubious penalty against Richard Carpenter for handling inside the box.
Top-scorer Constantine stepped up and confidently struck the ball into the net, sending goalkeeper Wayne Henderson the wrong way.
Brighton almost pulled a goal back before the break when Andy Whing's long ball from the right eventually dropped for Tommy Fraser whose neat shot beat Mark Goodlad but not his right post.
Henderson was caught on the back foot in the 55th minute when a failed clearance fell straight to the feet of Constantine, but the in-form player was too patient with his shot and allowed the goalkeeper to recover.
The visitors finally created a threatening opportunity in the 66th minute when Alistair John cut inside from the right and struck a powerful shot from 20 yards that Goodlad saved with an outstretched leg.
Sodje's tireless running was almost rewarded with a goal when he hammered a 25-yard firecracker towards goal but the ball flew inches wide of Henderson's left post.
The Seagulls pulled one back in the 84th minute when after Colin Miles headed the ball against his own crossbar, Fraser pounced on the rebound to stab past a helpless Goodlad.