The Saints were favourites going into the match-up against a downhearted Hammers side, fresh from an opening day thrashing at Manchester United, and it was rightly proven inside the first eleven minutes as forward Manolo Gabbiadini opened his season's account.
Controversy seeped in when Marko Arnautović received his marching orders just past the half-hour mark for aggressively elbowing defender Jack Stephens, before Dušan Tadić doubled the hosts' advantage from the spot after Steven Davis was brought down by centre-half José Fonte.
Pellegrino's nerves crept up in the second-half as Javier Hernández netted twice for the Hammers to bring it back to 2-2, but much to the Southampton manager's delight, Charlie Austin stepped up to the penalty spot in added time to ensure victory after Pablo Zabaleta had pulled Maya Yoshida to the ground inside the box.
Whilst many will argue the referee, Lee Mason, was the centre of attention, Southampton supporters will certainly be pleased that the Saints nervously got the victory they deserved and take their tally up to four points from a possible six under Pellegrino.
What were the positives to take from the win?
Just as they did in the opening weekend at home to Swansea City, it was Southampton who were unquestionably the dominant side throughout the 90 minutes.
Chances are definitely not a shortage for the Saints having created 14, and five of those were effectively on target, much to the boss' satisfaction.
West Ham played a helping hand in the home side's win after going down to 10 men before the interval. However, even with both teams equal in numbers, it was Southampton who were more likely to find the first goal.
Gabbiadini was the major threat for the hosts and the supporters will be hoping he can add to his Premier League tally in the coming weeks and months.
Conclusively, goals won't be an issue for Pellegrino's men this year - especially improving on their miserable record of not scoring on home turf since 5th April, or in footballing terms, 576 minutes of play.
Where do the Saints still need to work?
Even with the three points in the bag and unbeaten from their opening two Premier League fixtures, Southampton should be concerned about their defensive display.
Despite finishing the game with two thirds of possession, the men in red and white were second best in the shots category; the Hammers accumulating a superior 16 efforts at goal, with eight on target.
This will turn out to be a damaging issue for Pellegrino if he does not work on hi side's defensive play in training. They cannot allow their opponents so many opportunities on goal.
Although, saying that, the Saints won't come across a more prolific goal scorer in the box than Hernández, whose total of 39 Premier League goals have all been finished from within the area.
Nevertheless, the absence of Virgil van Dijk, a seemingly inevitable departure before the window closes, is significantly obvious and if Southampton are eager to improve or equal last season's 8th-placed finish last term, then the want-away centre-half desperately needs replacing.
What should Southampton fans expect moving forward?
The Saints have two fixtures to come before the international break at the tail end of this month; firstly a home tie to Championship outfit Wolverhampton Wanderers in the Carabao Cup but then they face the long journey up north to top-flight new boys Huddersfield Town next weekend.
Supporters will appreciate the fact that boss Pellegrino will prioritise league over cup competitions, so it is unsurprisingly expected that the Argentine will make several changes for the visit of Wolves.
However, Southampton could - and should - go unchanged for the journey to Yorkshire as both performances to this point have been nothing less than encouraging and the goals will come with consistency.
Adding to that, the quicker the situation regarding van Dijk is sorted then the better it will be to reinforcing the squad ahead of the summer window closing.