The Hammers struggled to get going against the Canaries and slipped into a precarious position in the match.
Goals from Robbie Brady and Wes Hoolahan gave Alex Neil’s side a commanding lead to protect, but West Ham showed their fighting spirit to come back.
The Hammers pulled one back after Victor Moses powered past three Norwich defenders, before his shot diverted into Dimitri Payet’s path and the French midfielder made no mistake from close range.
Noble then completed the comeback by scoring with a wonderful finish from the edge of the area.
West Ham could actually have won the match, had Emmanuel Emenike taken his late chance, but Slaven Bilic’s side should feel satisfied with a point hard earned.
And Noble was happy to celebrate the draw on social media site Twitter.
West Ham are now in seventh place in the Premier League table with 12 matches remaining.