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  The home side, leading by 136 on first innings, wobbled to 153-7 before Moeen's 59-ball knock took them 224-8 when rain forced an early close.
  Under-fire opener Keaton Jennings managed only 18.
  South Africa were earlier bowled out for 226 and will begin day four 360 runs behind.
  The Proteas already need to break the record for the highest successful run-chase on this ground, with the pitch showing further signs of turn and uneven bounce.
  England, 2-1 up, are chasing their first home series win against South Africa since 1998.
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  Bar captain Joe Root, who made a typically unflustered 49, none of the England top order were able to take advantage of home side's superior position in the game.
  Collectively, South Africa's attack was excellent, none more so than pace bowler Duanne Olivier, who picked up three wickets in the Manchester gloom.
  When Jonny Bairstow became the seventh wicket to fall, England were 289 ahead and in danger of letting South Africa back in.
  Moeen, though, counter-attacked, dishing out some particularly brutal treatment to the previously economical Keshav Maharaj.
  Targeting the leg side, left-hander Moeen hit the left-arm spinner for three sixes, sharing an eighth-wicket stand of 58 with Toby Roland-Jones, who contributed 11.
  When the rain arrived at 17:15 BST, Moeen had taken 38 runs from the previous 22 balls he faced.
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  South Africa began the day on 220-9 and lost their last wicket when Olivier top-edged to Bairstow.
  Trailing by such a large margin, they needed everything to go their way with the ball and, though the bowlers played their part, they were not always backed up in the field.
  Jennings was dropped by Dean Elgar at third slip and Dawid Malan put down by a diving Temba Bavuma, with Kagiso Rabada the unfortunate bowler on both occasions.
  A potential Ben Stokes edge off Morne Morkel did not result in an appeal, with the same batsman put down by Heino Kuhn at short mid-wicket off Olivier.
  Bairstow and Roland-Jones also survived tough chances to Hashim Amla and Faf du Plessis respectively.
  None were particularly costly in terms of runs, but the same cannot be said about an edge from Moeen off Maharaj to Elgar at slip, which just about carried. Moeen was on only 15 at the time.
  This was perhaps a last chance for Jennings, who averages 15.87 in eight innings in this series.
  The Durham left-hander, the 11th different partner for Alastair Cook since 2012, had not scored when he was given a life by Elgar and battled for more than an hour before lunch.
  Soon after the break he slashed at Rabada to be held at first slip by Amla.
  If his place is the one that is most under-threat, then the other new batsmen in the England side still have work to do in order to establish themselves in Test cricket.
  Tom Westley, who made a half-century on debut in the third Test, made only nine before edging a drive off Morkel, already a familiar dismissal.
  Malan, who has managed just 35 runs in four innings, tamely inside-edged to short leg off Maharaj for six.
  Ex-England captain Michael Vaughan: "Maybe for Jennings it is best that he steps out of the pressure cooker, goes back to Durham and work on things.
  "I think he has got better, he played a few nice defensive shots and a nice shot to cover, but he's not doing it consistently.
  "Early in his innings he doesn't get his weight back on the ball.
  "Who replaces him? Hameed was poor for Lancashire today, Stoneman would be next in line I think."
  Former England spinner Graeme Swann: "Calls for Ian Bell to return? I don't think he will.
  "His big chance was the first few games of the season and to score runs then.
  "You've got to look at why players aren't picked, because someone at the top doesn't rate them. Personally, I think he is one of the best players ever, but by the end he just wasn't scoring heavily enough.
  "I just can't see it."
target: Moeen Ali's thrilling, unbeaten 67 cemented England's stronghold over South Africa on day three of the final Test at Old Trafford.