However, he was powerless in the second innings as Curtly Ambrose tore through the tourists' batting line-up taking eight for 45 to bowl England out for 191 and hand the hosts a 164-run win.
Especially if they take England to victory, as they should, over the rest of this match.
But it was England who had the last laugh on a remarkable day at Lord's that saw 19 wickets fall in total.
Worcestershire's Moeen, 30, has batted in every position from one to nine for England as well as often being the sole spinner in the side. Moeen offered the greatest threat, in part because he was so miserly.
He became the sixth Englishman to score a century in his first Test as captain and admitted it was special. Temba Bavuma fell to Moeen Ali in similar vein in the next over. The other contender was Root himself, given that he scored 190 on a surface that those who came to the crease at the weekend reckoned to be untrustworthy.
Root was not without his luck during his 227-ball innings as he was twice dropped in the morning session before being stumped off a no ball on 149. However, if there were any doubts, Root put those to bed with a dogged and classy Day 1 display.
As ever with Cook, though, it was substance rather than style that counted - and in his first match since relinquishing the captaincy, England had good reason to be thankful for his efforts once again.
In fact, all three wickets South Africa threw were soft dismissals. Against Morne Morkel he essayed what seemed to be a textbook forward defensive except that the ball flicked the outside edge to give the keeper a simple catch.
In between times, Dawson bagged a pair when he was surprised by Rabada's full toss and lost his middle stump.
Hampshire left-arm spinner Liam Dawson, on his home debut, made the initial breakthrough with just his second ball Saturday when Rabada (27) edged to wicket-keeper Jonny Bairstow.
Bairstow has hit a half-century in all but one of his last five Tests - maintaining his standards even through England's losing run in India last winter, falling only a single short in his one match without a half-century.
Thereafter the catches kept sticking.
Even so‚ how South Africa might go about engineering victory is hard to fathom‚ especially as they will bat last on a pitch that is deteriorating quickly. Moeen accepted a firm straight drive from Dean Elgar off his own bowling, as well as an inappropriate pull from Duminy at square leg to ensure that when tea was being sipped the England players could contemplate drinking something stronger later in the evening.
Philander didn't bowl but should return to the attack on Sunday, although the Proteas already will be resigned to simply saving the test.