England win meant that formidable South Africa were also knocked out of the global event, rendering Proteas final match against the 2014 champions as one of academic interest.
Courtesy Jos Buttler's unbeaten 37-ball-66, England piled up a challenging 171 for four after being put into bat and then managed to restrict the Island nation to 161 to end their group league engagements with six points from four games.
Chris Jordan bowled a brilliant penultimate over to finish with figures of 4/28 in 4 overs while David Willey chipped in with 2/26.
With West Indies in all likelihood to win against Afghanistan in their final group league outing, the England team, who are likely to finish second in the group, will take on New Zealand in the semi-final at the Feroz Shah Kotla on March 30.
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Defending champions Sri Lanka are going through a very transition phase as they have won only two of their last 10 T20 internationals. The more embarrassing piece of statistic is the fact that the two wins have come against associate nations Afghanistan in this World T20 and United Arab Emirates in the Asia Cup.
Mathews kept the strike with him but could not get the desired big shot and played as many as four dot balls. He threw his bat in disgust at the end of the match.
At the start of the chase, Tillakaratne Dilshan (2) was out third ball trying to pull left-arm seamer David Willey. Dinesh Chandimal (1) chased a Chris Jordan delivery that could have been left alone only to guide into Buttler's gloves.
It became 15 for four as Lahiru Thirimanne (3) was brilliantly run-out by Ben Stokes. It became a catch-up game for the Lankans after that despite a valiant 80-run stand between Chamara Kapugedara (30) and Mathews.
In the 12th over, Kapugedara and Mathews took 21 off leg -spinner Adil Rasheed hitting him for three sixes. But in the next over, Kapugeedara was holed out in the deep as Sri Lanka were reduced to 95 for five.