The right-arm pacer, however, said he could not care less who closes out the Proteas innings as England continue on their path towards a 3-1 series win.
The opener will emerge from the South Africa series with an average of 15.87 in his eight knocks and that is taking into account some huge slices of luck.
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The off-spinner's intervention was badly needed as Hashim Amla (83) and Faf du Plessis (61) hinted briefly at significant resistance, and even sowed fleeting doubts about the inevitability of a home win as they got worryingly comfortable in a fourth-wicket stand of 123.
England were 134/6 when Moeen entered the fray, another spirited performance from Morne Morkel and Keshav Maharaj, this time ably supported by Duanne Olivier and Kagiso Rabada, giving South Africa the smallest of feet in the door as they attempted to mount a surprising comeback.
On a attractive sunny morning at the Emirates Old Trafford, the hosts didn't take long to get the final wicket of the Proteas innings as they were bowled out for 226 giving the home side a lead of 136 runs.
The corresponding South Africa record is 414 for four - the second-highest fourth-innings total to win a Test of all-time - against Australia at Perth in 2008.
And England went into lunch with a spring in their step as, from the final ball of the morning, Temba Bavuma (12) was adjudged caught behind following a review from Joe Root, despite an initial lack of appeal from bowler Toby Roland-Jones (1-52).
"That is [potentially] the way going forward - I think it is important to assess conditions but we have looked very risky over these last two games".
Bairstow and Ben Stokes also failed this time, but at crucial points in this series the late-order trio of Bairstow, Stokes and now Ali has come to England's rescue to stave off South Africa. Before Ali's entrance, England was in some trouble at 129-5 and then 153-7.
"They have only got three Tests against West Indies to do it but England don't panic and they will want to give these guys time".
"I just went with the flow".
There's likely more to come from Ali, too, as he ended unbeaten and took England to stumps on Day 3 on 224-8, a slightly wobbly second innings but enough to open a convincing lead with two days to play.
With that, the Proteas were all but done.
"The quality of the English bowling attack was superb in this series - they were relentless".
"I have felt I have got a lot of consistency".
He started this series as England's designated "second spinner", when Liam Dawson (remember him?) was drafted in to shore up their options for Lord's and Trent Bridge.
Earlier, England resumed on 260 for six after winning the toss.
First Root scrapped his way to 49, Stokes to 23 and then Moeen took over.