The Proteas, who had scored 189 for 2 after being sent in to bat, needed to restrict England to 131 to overtake Australia in net run rate and qualify for the semifinals but it was not to be their day.
Kagiso Rabada sent back England's Chris Woakes, skipper Eoin Morgan and Chris Jordan for the tournament's third hat-trick.
The Scots have lost all four Super 12 Group 2 games since defeating Bangladesh in the qualifiers last month.
Only veteran seamer Trent Boult, with eight victims, has claimed more wickets for New Zealand at the tournament.
Scotland, who are already out of the tournament, will be facing table-toppers Pakistan in their last Super 12 game at Sharjah on Sunday.
Ravindra Jadeja says that it is unfair to judge the current Indian team on the basis of one or two defeats after consistent good performances at home and abroad in the last three years.
Kohli though regretted the fact they could not play their usual dominant games against Pakistan and New Zealand.
India's seasoned bowlers then made short work of the unheralded batting line-up with both Mohammed Shami and Ravindra Jadeja returning with identical career-best T20 figures of 3 for 15.
Bumrah surpassed Yuzvendra Chahal (65 scalps) to now become India's highest wicket-taker in shortest version.
Namibia did well to put New Zealand in a spot of bother at 87/4 but gave away 73 runs in the last five overs.
India have brought back spinner Varun Chakravarthy by dropping all-rounder Shardul Thakur.
India will next lock horns against Scotland at the Dubai International Stadium on Friday, November 5.
With four wins in as many Super 12 games Pakistan became the first team to reach the last four from Group 2.
After being trounced by England, Mahmudullah's side had the West Indies on the ropes, opting to bowl first and reducing their opponents to 64-4 in 12.4 overs.
For the Men in Blue, Ravindra Jadeja and Hardik Pandya played the innings of 26* and 23 respectively as and no Indian batter crossed the 30-runs mark.