Dillon Morse and Cedric Main netted to hand the Mariners a two-goal advantage which was halved midway through the first half as the hosts attempted a comeback.
Shields stood firm, though, and held off some late Warrington pressure to climb to second in the Northern Premier League.
It was a difficult test for Phillips in his first game as a manager, with the Yellows having lost just one of their previous 14 league matches to climb to fifth.
A fast start was the order of the day and the Mariners delivered just that to quickly establish a smile on Phillips’ face.
On 13 minutes, Nathan Lowe’s corner was hooked goalwards by Robert Briggs and blocked before JJ Hooper was also denied by a defender. This time the ball bounced to Morse and his header had enough power on it to beat home goalkeeper Daniel Atherton and get the Phillips era off and running.
One quickly became two when Main darted inside from the left channel and rifled a low strike which took a nick off a defender and flew past Atherton as the forward netted his first goal for the club.
It was a dream start and the Mariners almost established what might have been an unassailable advantage midway through the first half as Briggs was played in on goal and rounded Atherton, but just as he was about to find an empty net he was denied by a tremendous last-ditch tackle by Evan Gumbs which kept Warrington in the game.
That point was emphasised just three minutes later when the Yellows halved the deficit, with James Baillie’s scuffed effort from the right of the area prodded in by the lively Luke Duffy from close range.
The goal buoyed the home side and they threatened an equaliser when Jordan Buckley cut inside from the left, but his powerful shot from outside the box went wide.
Shields re-established control and could have gone further ahead in what was a bright start to the second half, but Briggs whipped a shot wide from the edge of the box, a cross-shot from Will McGowan was tipped wide by Atherton and Hooper curled narrowly past the post.
Shields were in control and their cause was aided with 16 minutes left when Warrington’s James Harris was sent off for two bookings.
However, the hosts threatened with some direct play in the closing stages and went close when Sean Williams' sweet strike from 20 yards went just wide.
The Mariners held firm to see the game out and secure a third consecutive victory, and they will bid to maintain their momentum on Tuesday when they take on Witton Albion at 1st Cloud Arena.
South Shields: Moloney, Rose, Adams (c), McGowan, Morse, Bodenham, Tee, Lowe, Hooper (Osei 64), Briggs, Main (Kempster 78). Subs not used: Shaw, Jenkins, Hodgson.
Goals: Morse (13), Main (16).