Saints held by Hammers in stalemate
Southampton's English striker Rickie Lambert heads the ball during the English Premier League football match between Southampton and West Ham United at St Mary's Stadium in Southampton, southern England, on September 15, 2013.
Mauricio Pochettino's team had the better of the few chances on offer, but Jaaskelainen made several fine saves to ensure a dour encounter ended in stalemate.
West Ham's only real chance fell to James Collins in the closing minutes, but the Welsh defender shot high over the crossbar.
The draw left both teams in mid-table in the Premier League with five points from their four matches.
"We could have won it at the end when James (Collins) had his chance - that was the best chance of the game. It was a bit unlucky that it fell to our centre half, but from that far out he should hit the target," West Ham boss Sam Allardyce said.
"Overall, it was a decent performance. Defensively we showed how good we are but we can't hit the back of the net. That's my concern at the moment."
West Ham midfielder Mohamed Diame had an early sight of goal as he controlled a crossfield ball and tested Saints goalkeeper Artur Boruc.
But Southampton should have taken the lead with their first chance of the afternoon.
Jay Rodriguez's cutback from the byline found Dani Osvaldo unmarked, but the forward's goalbound strike was blocked by Jaaskelainen.
The Finn then denied Rickie Lambert as Southampton's England striker tried to convert from close-range.
West Ham captain Kevin Nolan had the ball in the net before half-time but his shot was ruled out for offside.
Kenya midfielder Victor Wanyama forced Jaaskelainen to tip over from distance shortly after the restart, with the opening goal almost coming from the resulting corner.
Adam Lallana swung the ball in and Lambert's powerful header rattled the post, followed by hopeful calls for a handball against Collins when Wanyama attempted to strike home the rebound.
Jaaskelainen superbly turned a Morgan 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 handball against Nolan rejected, with Wanyama firing the final chance wide.