Scienza fired Southampton ahead as the United backline failed to deal with the Brazilian’s direct play.
The Saints attacker was left in space to drive towards the box on the left-hand side before curling a shot towards goal with his right foot that took a wicked deflection off Oli Arblaster, wrong-footing the keeper and flying into the net.
Scienza now has four goals and four assists for Southampton in the league this campaign after joining from Bundesliga club Heidenheim in September.
Eckert’s side nearly doubled their lead after 20 minutes when Ross Stewart’s header on goal from a corner was cleared off the line by a diving Arblaster.
Five minutes before the break Saints dangerman Scienza broke down the left after a slip by Ki-Jana Hoever and cut inside before letting off a short from close range that was well blocked by Blades keeper Michael Cooper.
Cooper and Harrison Burrows then did well to scramble the ball clear and prevent a follow-up being poked home from six yards.
Sheffield United came close with a flurry of attacks just before the hour mark.
The Blades worked the ball well down the right before Hoever crossed the ball into Callum O’Hare who had a shot blocked behind for a corner.
Patrick Bamford had the best chance of the game for Chris Wilder’s side in the final minute of normal time.
He broke into the box down the left and cut inside and away from Elias Jelert before stroking the ball towards the far corner, but Saints keeper Daniel Peretz produced a great save, stopping the ball with his outstretched legs.