However, a further lengthy delay in the rain-affected four-day clash at New Williamfield, Stirling, means outright victory may be beyond them.
No play was possible on the third day until mid-afternoon but the Scots made up for lost time with a dominant display in the field to leave their rivals on 96-8 – 137 runs behind.
Having posted 233 in their first innings, Preston Mommsen’s side quickly took charge with three wickets during a deadly new-ball spell from Ali Evans and Safyaan Sharif.
Evans made the breakthrough with the second ball of the innings when he trapped Javed Ahmadi in front before Sharif chipped in with the prize scalp of the dangerous Mo Shahzad who chopped one on to his stumps.
The Scots really had their tails up when Evans clean-bowled Nawroz Mangal to reduce the visitors for 9-3.
It would have been 9-4 if Hamish Gardiner had hung on to a slip chance which would have cut short Ashgar Stanikzai’s stay at the crease.
Instead Stanikzai led a mini-recovery with Rhamat Shah as the Afghans rallied.
Gardiner’s lapse looked like proving costly as Stanikzai dispatched five boundaries during a spirited counter-attack.
However, Durham teenager Gavin Main joined the attack to remove him for 26 thanks to Con de Lange’s catch at mid-off.
Debutant De Lange’s day was to get even better when he was brought into the attack and proceeded to claim a wicket with his first delivery, Shah trapped lbw for 20. There was some resistance from Samiullah Shenwari who was unbeaten on 29 at the close but De Lange’s fine day continued with two more wickets while Main returned to pick up his second.
It left Afghanistan reeling on 94-8 and they will resume needing a further 137 runs from their last two wickets to deny Scotland the first-innings bonus points.
Earlier the Scots managed to add just six runs to their overnight total as Afghanistan quickly took the two wickets they needed.
Evans was first to go, deceived by a spinning delivery from Shah that knocked over his stumps.
Matthew Cross, whom the Scots hoped could add some useful late runs, instead was a victim of the same bowler, edging behind for 30.
SCOTLAND first innings (overnight 227-8)
MH Cross c Nawroz b Rahmat Shah 30
AC Evans b Rahmat Shah 3
GT Main not out 0
Extras (lb5, nb4) 9
Total (all out, 72.2 overs) 233
Fall: 1-12, 2-80, 3-102, 4-169, 5-180, 6-206, 7-224, 8-225, 9-232.
AFGHANISTAN first innings
Javed Ahmadi lbw b Evans 2
Nawroz Mangal b Evans 0
Mohammad Shahzad b Sharif 7
Asghar Stanikzai c De Lange b Main 26 Rahmat Shah lbw b De Lange 20
Samiullah Shenwari not out 29
Mohammad Nabi b Main 1
Mirwais Ashraf b De Lange 7
Yamin Ahmadzai c Evans b De Lange 0
Izatullah Dawlatzai not out 2
Extras (nb 2) 2
Total (8 wickets; 45 overs) 96
Fall: 1-2, 2-9, 3-9, 4-40, 5-73, 6-78, 7-94, 8-94