The result sees the academy side progress to the final of the Sussex Senior Cup, where they will face Eastbourne Borough at the Amex.
Worthing will however feel proud of their performance, and can take a lot of positives from the narrow defeat.
The Mackerel Men initially took the lead in the second half through Reece Meekums and looked the better side for much of the game, but Alfie Young's 85th minute sending off left Worthing with an uphill battle, and Jenks' late goal put paid to any hopes of a victory.
The first opening of the game fell to Worthing. Reece Meekums fired in a low effort from long range which was spilled by Hugo Keto, and Ollie Pearce raced towards the loose ball in the 6 yard box. Keto was able to recover just in time and divert the ball over the bar, but it was an early scare for the Premier League youngsters.
Far from being overawed by their million-pound opponents, the Mackerel Men approached the game with energy and attacking intent.
Another good chance fell to Worthing early on, this time through ex-Seagull Jesse Starkey. The ball fell to Starkey's feet in the box and the midfielder had a foot of space to set himself and drill a low shot at the near post, which Keto did well to keep out.
Young midfielder Ricky Aguiar went close on the 20 minute mark, firing a well-taken volley just wide from the edge of the area.
The Mackerel Men kept the pressure up as the half wore on, continuing to keep Keto on his toes. Pearce went close again with a powerful free kick from 25 yards, stinging the palms of Keto, before Starkey fired over the bar after some attractive one-touch build-up play to unlock the Brighton defence.
Brighton found their first good chance of the half through Taylor Richards. The striker made a darting run through the Worthing defence to latch onto a through pass and curled a shot towards the far corner, forcing temporary goalkeeper Jack Fagan into a terrific diving stop.
Reece Meekums, another ex-Brighton prospect, showed some fantastic skill to beat two men and open up some space, before firing just over the bar from range.
The half ended all square, but the Mackerel Men had looked the more dangerous side by far. Hinshelwood's men played with a much higher intensity than they had done in recent weeks, and carved out a plethora of promising openings. Brighton began to grow into the game as the half wore on, Richards looking particularly dangerous, but their chances were limited.
Brighton had the first real chance of the second half, and one which should have seen them take the lead. The Seagulls broke through Jordan Davies who released Richards through on goal down the left. He pulled the ball back for Romaric Yapi, whose shot looked destined for the top corner, but his strike hit a Worthing head and spun narrowly wide.
Jack Fagan was again called into action on the hour mark, making a fantastic stop at his near post to keep out Richards' fierce strike.
Worthing's first chance of the half came through a rocket from Aguiar. The midfielder picked the ball up 30 yards from goal and let fly, rifling a shot towards the corner and forcing Keto into a fabulous save to tip it round the post.
The resulting corner saw Worthing take the lead. The corner landed right in the middle of the box and Meekums snatched at the ball, poking it into the back of the net and sending the Worthing fans into raptures.
The opening goal seemed to kick Brighton into life, with chances for the Seagulls coming thick and fast after this. Just moments after conceding, they almost had an equaliser through Peter Gwargis, whose powerful strike thumped off the bar.
It took a world-class strike for the Seagulls to find their equaliser. Laurent Tolaj seemingly had no options and so chanced a strike from 30 yards. This turned out to be a wise choice, as his strike flew right into the upper reaches of the top left corner to bring them level.
Moments later, Brighton found themselves ahead through Haydon Roberts. The England U-18 international got his toe on the end of a stray ball after a corner, and poked the ball into the net via the post to make it 2-1.
Brighton's lead did not last long however, courtesy of Aarran Racine's formidable forehead. Aguiar swung in a pinpoint corner straight to Racine's head, and the centre back buried his header right in the bottom corner to bring Worthing level.
Worthing found themselves down to ten men with five minutes still to play. Yapi and Alfie Young grappled as the Brighton man looked to break through on goal, and both men tumbled to the floor. The referee saw Young as at fault, and showed the defender the red card.
The half ended with the sides still all square, leaving a tiring Worthing a tough half hour to play with ten men.
As could be expected, Brighton dominated proceedings. The pressure on Worthing's half was relentless, as the youngsters looked to make their man advantage count. Chances fell to Davies and Yapi, but Fagan's goal remained reasonably untroubled.
A minute after the second period of extra time, Brighton found their breakthrough. The ball was set for Teddy Jenks on the edge of the area, whose low strike took a large deflection and spun into the net past the helpless Fagan.
The game was over as a contest by then, with the men in red looking dead on their feet having given it their all for 115 minutes. The referee blew for full time and called an end to Worthing's valiant effort.
The fitness and precision of a Brighton side, who are among the best prospects in the country, proved too much for the Isthmian Premier side. Their focus will now shift back to the league, as they host Wingate & Finchley on Saturday, in search of a crucial three points.