Substitute Nathan Dyer broke the deadlock with a volley on the stroke of half-time, with an own goal from Newcastle right-back Mathieu Debuchy and a late Jonjo Shelvey strike completing victory.
Everton swept into second place in the Premier League with an impressive 3-0 victory over 10-man Swansea on Saturday.
Swansea City made sure of their place in the Premier League for next season and sent Blackburn a step closer to the drop with a 3-0 victory at the Liberty Stadium.