The forecast for Tuesday suggests that England will need to finish the game in four days if they want to seal a third victory in the series, and although they do not need it to retain the Basil D'Oliveira Trophy, South Africa's target already looks too great in the conditions.
Like Jonny Bairstow's 99 in the first innings, Ali's brisk half-century ensured England didn't succumb when under pressure, this time at 153-7.
England denied any formal approach had been made for the 48-year-old Bajan, who previously coached his native West Indies and is in his second spell in the European Central Bank set-up, but it seems highly likely that picture will change next week.
Jimmy Anderson put England in firm control on the second day of the fourth test at Old Trafford on Saturday, with his four wickets leaving South Africa trailing by 142 runs with just one first-innings wicket remaining.
He was fortunate to be dropped on 15 by Dean Elgar at slip off Maharaj but, with that let-off behind him, went on to bring up a fifty with a towering six that was caught on the players' balcony by a beaming Bairstow.
England vs South Africa Live Score 4th Test Day 3: England set for big lead against South Africa.
But Moeen took the game to the left-arm spinner, putting on a 58-run partnership with Toby Roland-Jones and eliminating the concern over the rough with positive footwork. Moeen was especially severe on Maharaj, hitting him for three resounding sixes. Saker is now the Baggy Green's fast-bowling coach and is set to face his old employers this summer.
"I felt like I couldn't bowl badly, certainly this morning", he said.
The ECB said they had not been approached by Cricket South Africa and would not consider the matter until the end of the Investec Series, which concludes early next week.
Broad had earlier claimed the final wicket of South Africa's first innings.
James Anderson took 4-38 at his home ground and Broad 3-46.
England have just three tests against the West Indies in which to settle on their lineup for this winter's Ashes squad, and it is entirely reasonable to say they can be no clearer yet about the staffing of much of their top and middle order.