The French defender powered home a first-half header at the Amex Stadium on Saturday to extend the Sky Blues' winless streak to eight games and leave them six points away from safety.
A piece of good fortune helped the Seagulls take the lead seven minutes in when the ball cannoned into the net off Coventry defender Richard Keogh after Craig Mackail-Smith's shot had been saved by Joe Murphy.
The visitors acquired teenager Grant Gardner on loan from Aston Villa on Thursday and reaped the rewards just nine minutes into his debut as he headed them level.
But it was Vincelot, who had replaced the injured Marcos Painter moments after Gardner's equaliser, who grabbed the winner, heading in Liam Bridcutt's free-kick eight minutes before half-time.
The Sky Blues travelled to Brighton having failed to win on their travels this season and they made life difficult for themselves by falling behind early on.
Captain Sammy Clingan played a woeful ball Keogh's way which Mackail-Smith ran on to. The Scotland international's initial effort was parried away by Murphy but the ball ricochet back off the Coventry centre back and rolled into the empty net.
The visitors responded instantly with debutant Gardner powering in a back-post header to equalise two minutes after the opener.
Brighton boss Gus Poyet was then forced into an early substitution when Painter came off for Vincelot after the defender pulled his hamstring.
The Seagulls fans felt they should have been awarded a penalty when Clingan, desperate to make amends for his earlier error, grabbed hold of Billy Paynter as he entered the penalty area, but referee Gavin Ward gave a free-kick on the edge of the box.
That set-piece came to nothing, but it was another free-kick which ensured Brighton regained the lead.
Gardner brought down the lively Craig Noone, presenting Bridcutt with an opportunity to send the ball into the box.
Referee Ward would not allow the Seagulls midfielder to take the free-kick quickly and that proved to be a blessing in disguise as Bridcutt eventually found Vincelot who headed in.
Nobody in a Coventry shirt tracked the Frenchman as he ran into the box and steered his header into the far corner of the net from just inside the penalty area.
Andy Thorn's side continued to be wasteful in front of goal in the second period, failing to profit from Chris Hussey's inviting crosses. Leading marksman Lukas Jutkiewicz was the biggest culprit,
firing wide on a number of occasions.
Poyet's side, who had only won once in their last 12 outings, continued to invite their opponents forward but they could not find an end product.