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Bentley struck either side of half-time to put the home side in control before Nic McDonnell's 70th minute goal set up a tense finish.
As Bromley threatened to grab an equaliser, substitute Ndumbu-Nsungu settled the home fans' nerves with a late double.
Bromley more then matched their League One opponents in the opening stages and should have held a man advantage when, after only ten minutes, Gillingham captain Michael Flynn clearly hauled back McDonnell as the striker raced through on goal.
Referee Keith Hill simply waved away the protests of the Bromley players, much to the dismay of the travelling supporters and manager Mark Goldberg.
Gillingham were forced into a change on 27 minutes due to an injury to centre-half Leon Johnson who was replaced by the fit-again Brent Sancho.
And Sancho's introduction appeared to galvanise the home side who finally carved Bromley open to take an undeserved lead.
Matt Jarvis, a peripheral figure until now, found Gary Mulligan in the area with a deflected cross and the striker flicked the ball on to Bentley to head home from a yard out.
Bromley continued to pose a threat after the interval and Kelvin Jack had to be alert to beat away Sam Wood's thumping volley from 20 yards.
But a minute later Bentley was on hand to tap home a decisive second goal after Dean McDonald had flicked on Clint Easton's cross.
The contest appeared over, but in the 70th minute McDonnell raced on to substitute Gareth Williams' precise through ball and produced a calm finish beyond Jack to revive Bromley's hopes.
But after Jack had saved Williams' long-range effort, Ndumbu-Nsungu tapped home another Jarvis cross to end Bromley's hopes.
And the afternoon got better for the Congolese striker in the final minute when he pinched the ball off Francis Duku in the area and curled a fine shot beyond Andy Walker's despairing dive.