That left Moeen Ali stranded on 75no - the left-hander's dynamic contribution seemingly putting the game beyond South Africa's reach, given The highest successful run-chase at Old Trafford remains the 294 scored by England against New Zealand in 2008.
Morne Morkel took two wickets for one run in four balls on Monday as he dismissed Stuart Broad and James Anderson to end the innings after England resumed on their overnight 224 for eight.
England were bidding for a first home Test series win over South Africa since 1998 at 2-1 up with one to finish in this four-match contest.
South Africa first arrived in England for the one-day worldwide series in May, but Maharaj is sure no-one in the squad is thinking of home at this stage, with two days still remaining.
Live coverage of the fourth Test between England and South Africa continues on Sky Sports Cricket - with over-by-over commentary and in-play video clips on our live blog, available on Sky Sports digital platforms.
Pace bowler Olivier, only called up for this match after back injuries ruled out both Vernon Philander and Chris Morris, had taken two wickets for 13 runs in eight overs.
Elgar actually got the ball rolling - or dropping - when he gave Keaton Jennings a life on nought.
Malan, who has 35 runs at 8.75 in his first two Tests, was also dropped on three by Temba Bavuma in the deep after playing a wild shot to Rabada.
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I have given everything, but that has not been reciprocated, so I can't stand it any longer. "I can not continue this way".
But South Africa-born Jennings was unable to cash in on his reprieve.
Dean Elgar's drop of Moeen, at slip off Maharaj, was the worst of the lot given the match situation and the fact he actually had the ball in his grasp before rolling over and then releasing it.
Bairstow's enterprising and entertaining knock ensured England made a solid first-innings total of 362.
The current lead of 360 is more than any team has successfully chased in the fourth innings at Old Trafford.
Malan, who so impressed England's management on his Twenty20 worldwide debut this summer, did not look the part this time.
But his seventh Test at Old Trafford was the first fixture since what was known as the Pavilion End had been renamed in honour of Anderson, England's all-time leading Test wicket-taker.
Instead they are part of the lengthening tale of woe that is South Africa's too-long summer in England‚ where every series they have touched has turned to lost.
But Bairstow, playing some handsome strokes, put on a 50-run partnership with last man Anderson - with 46 of those runs coming from Bairstow.