Goals in either half from Alexander Tettey and Alexander Soderlund boosted Norway's men to a 2-0 victory over Group H also-rans Malta in Oslo, but Per-Mathias Hogmo's men have not done enough yet to qualify for Euro 2016.
Norway are two points clear of Croatia in second place but should they fail to win at Italy on Tuesday, Croatia would qualify automatically with a win over Malta.
Norway took control from the off and almost scored through Even Hovland's header in the fifth minute.
They grabbed their first goal almost 20 minutes into the game, Tettey getting his outstretched leg to Hovland's saved shot while Andrew Hogg was still sprawling.
Per Ciljan Skjelbred, Soderlund and Jo Inge Berget -- the latter going closest with a snapshot that Hogg did well to parry -- almost doubled the lead before the break.
Alfred Effiong might have equalised ahead of half-time but Orjan Nyland managed to tip his left-footed drive over the bar.
Norway went 2-0 up in the 52nd minute as Soderlund stroked home Markus Henriksen's clever pass from the left.
The Rosenborg striker went perilously close to completing a brace in the 74th minute but he scooped over.