Julian Okai, playing in an unfamiliar wide-right role to accommodate 15-year-old Lyle Della-Verde on the left, then slashed narrowly wide from Smith's short pass before Stevens swung a 25-yard effort past the post from Woodyard's precise ball in an electric start to proceedings.
United were given a reminder of their visitors' quality in the 13th minute as some lax play in midfield allowed Brighton to equalise. Both Stevens and Anthony Furlonge had opportunities to clear the danger, but eventually a fine move was rounded off by Jordan Woodley, who tapped in a left-wing cross at the back post.
It was to prove a momentary lapse for the hosts, even if Albion did enjoy a greater proportion of possession as a result of their standing in the match. Okai's fierce shot had to be pushed over at full extension by the visiting custodian after the winger had pressured a defender into miscontrolling Teddy Nesbitt's cross-field pass in the 27th minute, and Ofori-Acheampong followed that up by scooping over from Smith's knock-down.
Southend's second goal arrived eight minutes before half-time as Woodyard contributed his first youth team goal of the current campaign. The midfielder, later presented with the October Shrimpers Trust Youth Team Player of the Month award, was the beneficiary of Della-Verde's industry on the left flank with the tricky wide-man getting to the byeline before cutting back to Woodyard for a measured finish from eight yards.
The first period ended with Louis Baucutt powerfully connecting with a back-post header, only to send the ball across the face of the goal from Kane Ferdinand's flick-on.
Blues were deservedly in front at the break, but the destiny of the fixture was ultimately decided within sixty second half seconds. At one end, some excellent build-up play from the Seagulls saw George Hayward denied by a sprawling Daniel Bentley save by the base of the left-hand upright, and it was from the ensuing break that United scored their third.
Stevens and Della-Verde were at the heart of the move again, Stevens chipping forward for the trainee to fire goalwards on the volley. The goalkeeper appeared to have made a comfortable save, but he spilled the ball at the feet of the waiting Smith, and the Republic of Ireland Under-18 international squared for Ofori-Acheampong to drive his shot home.
Bentley again thwarted Hayward with a low stop just before the hour mark, but the Shrimpers were predominantly looking to add to their own tally as Ofori-Acheampong glanced a header wide and Woodyard sent a daisy-cutter past the opposite upright from the resultant goal-kick.
The 'keeper then made a brave block to stop Ofori-Acheampong from converting Okai's slide-rule pass, whilst Anthony Furlonge chipped over at the back post after Nesbitt flicked on Stevens' corner.
The away side were not without their own opportunities in the closing stages, a forward failing to nod home Chris Cumming-Bart's centre before the substitute himself rode a couple of challenges to bring a strong-handed save from Bentley. Leon Redwood also went close for Brighton, sending a curling free-kick onto the outside of the left-hand post, but there was to be no way back for the visitors.
Southend instead claimed their fourth League win in seven matches, although Ricky Duncan and his squad will now turn their attention to the visit of Brentford in the FA Youth Cup sponsored by E.ON. The Bees make their way to Roots Hall on Friday evening for a 7:30pm kick-off to face a confident Shrimpers outfit. Admission is £3 for adults and just £1 for concessions.
Southend United: Daniel Bentley, Anthony Furlonge, Teddy Nesbitt, James Stevens, Louis Baucutt, Kane Ferdinand, Julian Okai (Steven Camacho 88), Alex Woodyard, Duane Ofori-Acheampong, George Smith, Lyle Della-Verde (Reece Hall 66).
Substitutes not used: Ryan Auger, Rhys Mackay, Jack Paxman.
Goals: Stevens (2), Woodyard (37), Ofori-Acheampong (55).
League