Ngog pounced on a Chung-Yong Lee through-ball after 36 minutes before rounding Lee Camp to open the scoring. Beckford sealed the win in stoppage time, running clear of the Cherries defence before seeing his shot deflected over the onrushing Camp.
The game, featuring the two youngest managers in the division, started brightly with both sides attacking from the off.
Dougie Freedman's side have been on a mini revival of late and pushed hard for the opener with Beckford and Neil Danns going close early on.
Former Blackpool defender Alex Baptiste then saw his 11th minute pile driver well tipped over the bar by Camp, who joined Bournemouth on loan from West Brom in the week.
One minute later left-back Baptiste drove into the box once more but his goal-bound shot was deflected over by Shaun MacDonald.
Eddie Howe's men then kicked into life with the lively Tokelo Rantie, yet to score in eight games, forcing Andy Lonergan into a smart stop.
The keeper was back in action moments later to deny Ryan Fraser in an end-to-end contest in chilly conditions at the Goldsands Stadium.
After ex-Liverpool player Jay Spearing had ballooned a glorious chance over the bar on 24 minutes, Ngog got his goal to put his side one up despite Camp making a last-ditch attempt to keep the ball out.
The visitors, whose only other league win came against Birmingham in their last away game, held out firmly until half-time.
After the break the game carried on at a ferocious pace and Ngog looked set to make it 2-0 before a lunging Steve Cook intervened after 59 minutes.
Cherries top-scorer Lewis Grabban had a shot blocked just before the hour before Eddie Howe brought on the cavalry after 63 minutes, introducing Brett Pitman and Wes Thomas.
But his team still struggled to create clear openings with a Charlie Daniels effort blazing over the bar after 67 minutes the closest they came for much of the second half.
Pitman curled a free-kick narrowly over late on before Thomas, making his 150th career league appearance, shot wide from 12 yards.
Bolton were not hanging on though with Beckford making a nuisance of himself upfront. Danns missed a chance to seal it with three minutes left but that honour went to former Leeds striker Beckford, who celebrated wildly with the away fans.
Bournemouth huffed and puffed but failed to maintain their record of scoring in every league game so far this season.