The 38-year-old Jaaskelainen proved decisive again in the 49th when he tipped the ball out for a corner from Victor Wanyama's volley. The Finnish goalkeeper then made a stunning one-handed diving save to parry Morgan Schneiderlin's volley in the 67th.
Even in-form England striker Rickie Lambert, who hit the post with a header early in the second half, couldn't beat Jaaskelainen as his right-foot strike was also denied six minutes later.
"We're creating chances and we just have to start putting them away," Jaaskelainen said. "We get one goal and that confidence will come. But I'm happy to keep clean sheets."
West Ham wasted its best chance of the match with six minutes to go as Mark Noble served up a fine cross in the area for James Collins, only for the defender to drag his shot over the crossbar.
"We could have won it at the end when Ginge (James Collins) had his chance, that was the best chance of game," Allardyce said. "It was a bit unlucky that it fell to our center-half, but from that far out he should hit target. 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."
Both teams now have five points from four games, four less than league leader Arsenal, which is level on points with Tottenham after a 3-1 win at Sunderland on Saturday.
Liverpool can reclaim the first spot and maintain its 100 percent record in the league with a win at Swansea on Monday night.