Miraz and Nayeem looked set to continue when the heavens opened up, which saw the umpires take the players off the field and resulted in the tea break being taken early.
The start of the final session was temporarily halted as an inspection was scheduled and the covers were removed.
However, with the new ball available, light intervened. South Africa were asked to bowl spin only due to the fading light, as taking the new ball and introducing their seamers ran the risk of the players being taken off the field.
The Bangladesh batters took a liking to South Africa using their spinners and the old ball, stretching their lead beyond 80 runs, but light intervened again as the players went off for a second time.
Despite two further light checks by the officials during the delay, things did not improve and stumps were finally drawn just before 4pm Bangladesh time.
Century partnership sees Bangladesh fight back in Test against Proteas
Home side have a lead and three wickets in hand in low-scoring Test at Sher-e-Bangla National Stadium in Dhaka
Image: Darren Stewart/Gallo Images/Getty Images
A crucial century seventh-wicket partnership between Bangladesh batsmen Mehidy Hasan Miraz and Jaker Ali catapulted their side to an important 81-run lead after day three of the first Test against the Proteas in Dhaka on Wednesday.
Miraz contributed 72 runs from 134 balls at Sher-e-Bangla National Stadium, while Ali chipped in with a dogged 58 from 111 balls to erase the deficit and leave Bangladesh on 250/7 before the tea break.
When stumps were eventually drawn due to bad light, the home side sat on 283/7 with a lead of 81 runs, with Miraz (87 from 111) and Nayeem Hasan (16 off 28) not out as South Africa had the option of taking the second new ball when play resumed on day four.
In a low-scoring game, if the hosts can put up a total close to 150, South Africa may struggle in their chase.
Bangladesh started the third day on 101/3, with Mahmudul Hasan Joy (38) and Mushfiqur Rahim (31) looking to kick on and erase the 101-run deficit.
Kagiso Rabada had other ideas, as he struck twice in the fifth over of the day, removing Joy for 40 and Rahim for 33 to leave Bangladesh reeling on 106/5.
Left-arm off-spinner Keshav Maharaj grabbed his second of the innings with the dismissal of Litton Das, reducing the hosts to 112/6, as Jaker Ali and Miraz joined forces with a deficit of 90 runs to reel in.
The duo put the Proteas bowlers to the sword, each scoring half-centuries to record a partnership of 138, taking their side to 250/6 and a lead of 48.
Maharaj made another important breakthrough when he trapped Ali leg before wicket, a decision the batsman sent up for review, but his request was unsuccessful as he departed the scene for a gritty 58.
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Miraz and Nayeem looked set to continue when the heavens opened up, which saw the umpires take the players off the field and resulted in the tea break being taken early.
The start of the final session was temporarily halted as an inspection was scheduled and the covers were removed.
However, with the new ball available, light intervened. South Africa were asked to bowl spin only due to the fading light, as taking the new ball and introducing their seamers ran the risk of the players being taken off the field.
The Bangladesh batters took a liking to South Africa using their spinners and the old ball, stretching their lead beyond 80 runs, but light intervened again as the players went off for a second time.
Despite two further light checks by the officials during the delay, things did not improve and stumps were finally drawn just before 4pm Bangladesh time.
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