The Brazil playmaker's quick-fire double cancelled out Nathan Redmond's scrambled goalmouth finish as the Hammers battled hard for victory at St Mary's.
If Anderson's angled drive for his first looked tidy, his imperious match-winning finish to cap a two-pass counter-attack blitz proved very easy on the eye.
The accomplished 25-year-old now has eight goals and two assists for the Premier League season: amid the post-Christmas malaise his was a performance of unrivalled poise and precision.
Ralph Hasenhuttl tasted defeat for the first time as Southampton manager, his manful Saints unable to string together three league wins.
West Ham boss Manuel Pellegrini will have been delighted to tiptoe home with all three points, especially given his injury-hit squad was so threadbare he could only fill six of the seven substitute berths.
Saints started brightly, probing with the purpose and vigour Hasenhuttl has so quickly instilled.
The hosts tired visibly as the half wore on, though, the festive rigours taking a clear toll.
The Hammers eventually eased into their stride, but only stepped on to waste the two chances of the half.
First Lucas Perez scuffed woefully wide when he should have buried Aaron Cresswell's low cross.
And then Robert Snodgrass curled wide from 18 yards with the goal at his mercy.
Redmond bundled home the opening goal in bizarre fashion after the break, with Fabianski denying Oriol Romeu twice and Redmond once before the ex-Norwich man finally ground the ball across the line.
The ugly goal proved in keeping with the night's post-Christmas sloppiness, but also served to jolt West Ham out of their slumber.
The Hammers jumped straight on the attack, and Anderson thumped in the equaliser after Maya Yoshida's poor clearing header.
Saints' bid for an immediate riposte bit hard, as West Ham struck again on a lightning counter.
Stuart Armstrong's blocked shot from distance after a corner saw Diop set Antonio free, and he in turn chipped through for Anderson.
The Brazilian collected, raced on and finished in style for a goal of high class.
Saints refused to roll over and grafted again in a bid for an equaliser, but to no avail.
Austrian boss Hasenhuttl has forced an immediate upturn in attitude having replaced the ineffectual Mark Hughes, but not even that new backbone was enough to help salvage a point.
Lemina drew a fine save from Łukasz Fabianski late on, albeit when offside, summing up the Saints' night.