After England stuck with the same XI that had lost the opener, Jason Roy (40 off 29 balls) and Jonny Bairstow (35 from 17) peppered the boundary rope following the early loss of Jos Buttler when they were asked to bat first.
There was a lull in the middle overs but Moeen thrashed three fours and four sixes, dominating a 51-run stand with Ben Stokes that spanned 17 legal deliveries and 14 minutes of the most ferocious hitting.
Stokes finished as England's top-scorer with 47 not out off 30 balls, with four fours and two sixes, as England amassed the second highest T20 international total at Kingsmead, but there was another failure for Joe Denly.
Scrutiny on Buttler's best position in the order seems set to heighten as well after he made just two, departing when he thin edged to wicketkeeper Quinton De Kock as Lungi Ngidi picked up where he left off in East London.
Bjorn Fortuin did not have much luck in dropping a sharp return catch off Bairstow, who unfurled a series of lovely drives as he and Roy took England from 20 for one after 3.5 overs to 55 for one at the end of the powerplay.
The Yorkshireman clattered back-to-back sixes off Andile Phehlukwayo as England continued to accelerate, but he was bowled through the gate later in the over to end a 52-run stand alongside Roy.
The introduction of left-arm wrist-spinner Tabraiz Shamsi put the brakes on, leading to Roy holing out as England reached 90 for three at the halfway stage.
While Eoin Morgan dispatched Shamsi for six over deep midwicket and Stokes did likewise to Dwaine Pretorius, they were rare successes for England in the middle overs as the South Africa pair strangled the scoring rate.
An off-balance Morgan clothed Pretorius to long-off for 27 off 24 balls before Denly was through his shot before the ball had got to him off Phehlukwayo, dragging on to his stumps in an ugly dismissal for one.
England had lurched from 90 for two to 125 for five but Moeen thumped Phehlukwayo over long-on from his second ball before thrashing six-four-six off Beuran Hendricks, who shipped 45 in three overs.
A remarkable sliced drive off Ngidi flew over deep backward point before Moeen sent a catch to long-on. The touchpaper had been lit, though, with Chris Jordan then clubbing Phehlukwayo straight over the rope.
Temba Bavuma pulled off a stunning catch on the run to see off Jordan in the deep, having spilled an earlier catch to reprieve Stokes, who carried England beyond 200 and what looks a formidable total in-between innings.