In a match devoid of many moments of class, the oldest man on the pitch proved decisive as Saints were denied a first home win of the season.
The 38-year-old was first called into action after 11 minutes, somehow keeping out a Dani Osvaldo effort when it looked easier to score – the best chance of a tepid first half in which Kevin Nolan had a goal ruled out for offside.
Rickie Lambert hit the post moments after play resumed, with the England international, making his 200th Southampton appearance, then denied by Jaaskelainen as Mauricio Pochettino’s side pushed for the opener.
The veteran Finn, supported impressively by James Collins and Winston Reid, was also at his best to stop Morgan Schneiderlin, who was lucky not to be booked in the first half for a poor tackle on Mohamed Diame.
Referee Andre Marriner chose not to even award a free-kick for that challenge and was in the spotlight again after adjudging a Joey O’Brien lunge on Adam Lallana only worthy of a booking.
Heading into the game, much of the talk revolved around Ravel Morrison. The highly-rated 20-year-old was handed his first Premier League start in place of Stewart Downing, who has joined Andy Carroll, Joe Cole and George McCartney in the treatment room.
Southampton brought in Nathaniel Clyne, Jay Rodriguez and Luke Shaw, with the latter almost caught out in the opening minutes. Diame impressively controlled a crossfield ball and turned the teenage left-back, giving him space to sting the palms of Artur Boruc.
West Ham were quickest to settle in miserable conditions on the south coast, but Saints should have taken the lead with their first chance of the afternoon.
After losing his man down the left, Rodriguez’s cute cutback from the byline found Osvaldo unmarked – but the Italian’s goalbound strike was impressively blocked by Jaaskelainen.
Diame saw an audacious long-range drive whistle just over as West Ham pushed for an opener in the rain, which they thought they managed just past the half-hour mark.
Boruc spread himself well to stop Jarvis when through one-on-one but captain Nolan rifled home from outside the box – only for the offside flag to cut the Hammers’ celebrations short.
Schneiderlin was fortunate not to receive a yellow card for a poor challenge on the already booked Diame, with West Ham furious as the midfielder left in pain on the floor without so much as a free-kick.
Lambert nodded over and Morrison curled just wide from 25 yards, before Marriner called time on a turgid first half.
Victor Wanyama, particularly poor in the first half, forced Jaaskelainen to tip over from distance shortly after the restart, with the opener almost coming from the resulting corner.
Lallana swung the ball in and Lambert’s powerful header rattled the post, followed by hopeful calls for a handball against the impressive Collins when Wanyama attempted to strike home the rebound.
Saints had seemingly given up on their attempts to threaten West Ham with aerial balls and reverted to playing on the deck, with Osvaldo slipping through Lallana only for Jaaskelainen to thwart him.
Pochettino’s side continued in the ascendancy and Schneiderlin saw a threatening overhead kick headed away by Reid after Osvaldo had seen a shot blocked.
Mark Noble and Wanyama were both booked for late challenges, with Joey O’Brien soon joining them for a tackle on Lallana that saw tempers fray and could have resulted in a red.
The challenge came after Jaaskelainen superbly turned a Schneiderlin volley around the post, with the veteran goalkeeper then brilliantly clawing away a curling Lambert effort.
Collins lashed over as West Ham pushed a for a late winner and Saints saw appeals for a handball against Nolan rejected, with Wanyama firing the final chance wide.