Thabo Mnyamane thought he had put Marumo ahead 14 minutes from time in northern city Polokwane only to be thwarted by Akpeyi, whose brilliant reflex save diverted the ball on to the post and away from danger.
The save came just after Chiefs had been reduced to 10 men when left-back Sifiso Hlanti was shown a second yellow card, then a red for pulling back an opponent who posed no immediate threat to Akpeyi.
Gallants also finished the match a man short as midfielder Celimpilo Ngema was sent off 10 minutes from time for kicking the ball into the stomach of injured Zimbabwe forward Khama Billiat.
Chiefs came close to snatching an undeserved victory at the death as Zimbabwe goalkeeper Washington Arubi spectacularly parried a point-blank Eric Mathoho header over the crossbar.
From the resultant corner, another Chiefs centre-back, Daniel Cardoso, headed wide to the relief of the home team.
Drawing lifted each club one place after matchday 5 in the richest African national league with a 15 million rand ($1 million/ 860,000 euros) first prize.
Chiefs rose to 12th, eight points adrift of pacesetters and defending Mamelodi Sundowns, and Marumo to 15h, above bottom club TS Galaxy on goal difference.
English coach Stuart Baxter was recently rehired by Chiefs to try and end a six-season run without a trophy by the club who have claimed a record 53 domestic titles since being formed in 1970.
But there have already been calls on social media for him to be fired after just one victory in five league matches and the early elimination from a lucrative knockout competition.
“We do not want goalless draws — we want to win matches. It was a difficult game with very few scoring chances,” said Baxter after the latest disappointment.
On Saturday, record 11-time Premiership champions Sundowns triumphed 2-0 away to Orlando Pirates through two second-half goals from Namibia star and 2021 Premiership Footballer of the Year Peter Shalulile.
Pirates rarely posed an attacking threat and a first league loss of the season left them fifth, five points off the pace.
Sundowns are two points ahead of SuperSport United and Stellenbosch, who achieved 2-1 home victories against Maritzburg United and Chippa United respectively.