After being handed his first Premier League start, Diego Gomez wasted little time in carving open the Bournemouth defence, providing a through ball for Kaoru Mitoma to steer wide.
But his next defence-splitting pass proved to be far more fortunate, as it led to the award of a penalty as referee Michael Oliver, who - perhaps harshly - ruled that Kepa Arrizabalaga had fouled Joao Pedro.
The Chelsea loanee was unable to make amends from the subsequent spot-kick, guessing the wrong way as Pedro calmly rolled the ball into the opposite corner.
One of the Cherries’ danger men, Antoine Semenyo, was presented with the chance to level the scoreline after the half-hour mark when he raced in behind the high Brighton line, only to fire his shot straight at the resolute Bart Verbruggen.
It was then Brighton’s turn to rue a missed opportunity, and it was Mitoma again who fluffed his lines, as he volleyed against the upright from Tariq Lamptey’s well-weighted cross, ensuring the lead remained a slender 1-0 following an entertaining first-period at the Amex Stadium.
The Seagulls offered stubborn resistance early after half-time, as they looked to frustrate a Bournemouth side that had entered the contest as the second-highest away scorers in the league.
With the hosts standing firm, it took a special effort from Justin Kluivert to restore parity in the 61st minute, with the Dutchman doing so after purposefully cutting in from the left flank and rifling an unstoppable strike out of Verbruggen’s reach.
That goal also made Kluivert the first Bournemouth player to score 10 away goals in a top-flight season.
Unfortunately for Kluivert, however, his historic moment counted very little, as substitute Welbeck restored Brighton’s lead within three minutes of his arrival, guiding the ball in off the far post after being sent through by Georginio Rutter.
Welbeck’s late strike sealed maximum points for Fabian Hurzeler’s charges, moving them up to eighth and level on points with seventh-placed Bournemouth.