All of the Tigers points came in the first half, with Will Hurrell and Johne Murphy scoring the tries.
But the visitors also had to survive a late scare when Saracens fly-half Alex Goode missed a penalty that would have snatched victory from Leicesters grasp.
Murphy continued his progress following a knee injury with a strong showing for 55 minutes at full-back, while Ayoola Erinle played just over an hour in his first game since the end of last season.
Goode had given the hosts a 3-0 lead from a sixth-minute penalty, but Hurrell continued his prolific start to the season with a try in the left-hand corner after good work along the backline from Sam Vesty, Erinle and Murphy.
The response, though, was almost instant and Sarries left-wing James Short grabbed their opening try after neat work by Goode who also struck the conversion from the left-hand touchline to give his side the lead again at 10-5.
Vesty replied with three penalties of his own after Saracens had been penalised at the breakdown and Tigers led again 14-10 after half an hour with Sarries flanker Joe Wheeler on the sidelines after receiving a yellow card.
It was Murphy who stretched the Tigers lead with a try at the ned of the opening period following forceful runs by Brett Deacon and Erinle. Vestys conversion made it 21-10 in Tigers favour at the half-time whistle.
But Tigers were unable to add to that tally in the second half and Saracens got within striking distance as Goode finished off a length-of-the-field counter-attack to score in the right-hand corner with just 10 minutes remaining.
His conversion reduced the gap to just four points and Goode also struck a solid penalty from 30 metres to set up the closing drama but, with his side trailing by a point, he pulled his final shot wide of the posts in the last minute.
Tigers host their first home game in the Guinness A League next Monday evening when Sale are the visitors to Welford Road (7pm). For details of how claim your match ticket, see the Tigers website from Thursday morning.
Leicester Tigers Development XV: 15 Johne Murphy, 14 Jack Cobden, 13 Ayoola Erinle, 12 Tom Youngs, 11 Will Hurrell, 10 Sam Vesty, 9 Ben Youngs; 1 Boris Stankovich, 2 Mefin Davies (c), 3 Santiago Bonorino, 4 Calum Green, 5 Dan Hemingway, 6 Josh Goldspink, 7 Rob Bell, 8 Brett Deacon
Replacements: 16 Greg Sammons, 17 Dan Cole, 18 Tom Armes, 19 Mark Deaville, 20 Sam Harrison, 21 Rickie Aley, 22 Manu Tuilagi
Saracens: 15 Noah Cato, 14 Edd Thrower, 13 Henry Staff, 12 Mike Stanley, 11 James Short, 10 Alex Goode, 9 Mickey Wilson; 1 Jordan Mitchell, 2 Alex Walker, 3 Tom Mercey, 4 Rob Anderson, 5 Harry Spencer, 6 Tom Wheeler, 7 Will Fraser, 8 Don Barrell. Replacements: 16 Jamie George, 17 Sam Staff, 18 Alex Casey, 19 Sean Vine, 20 Luke Baldwin, 21 Owen Farrell, 22 Jake Sharp
