Papiss Cisse had an opportunity at the other end in the 18th minute, but his left-footed drive from outside the area drifted over the crossbar.
West Ham broke the deadlock just before half-time, and it was former Newcastle favourite Nolan who put them in front. The midfielder rifled home from close range after good work by Joey O'Brien, but refused to celebrate the goal.
Newcastle almost hit back immediately after the break when Demba Ba jumped high in the box, but Jaaskelainen was equal to his header and West Ham cleared the danger.
The Hammers could have doubled their lead just before the hour mark through Gary O'Neil, whose powerful header from a Nolan cross was kept out by Tim Krul.
Newcastle put their opponents under intense pressure in the latter stages, swinging in successive corners and coming close through Shola Ameobi and Ba.
Andy Carroll had a great chance to score against his former club on 72 minutes when he latched onto a Nolan through ball, but Krul produced a brilliant save to keep the score at 1-0.
The Magpies bombarded the visitors goal in the latter stages, but couldn't find a way past Jaaskelainen as the visitors secured all three points.