Asllani had given Albania an early lead, but Lorenzo Lazzari's second-half equaliser threatened to leave the hosts frustrated before a late handball inside the San Marino penalty area presented Albania with a decisive opportunity.
Asllani gives Albania early advantage
Albania made the perfect start and took the lead in the 11th minute.
Kristjan Asllani finished to put Rolando Maran's side 1-0 ahead, giving the hosts the early control they had been expected to enjoy against a San Marino side still searching for their first point of the Nations League campaign.
Despite Albania's advantage, San Marino managed to keep the deficit to a single goal going into half-time.
San Marino hit back
The visitors produced a surprise response after the interval.
Lorenzo Lazzari scored in the 66th minute to level the contest at 1-1, leaving Albania facing the prospect of dropping points in a match they had been expected to win comfortably.
San Marino defended stubbornly as Albania searched for a late breakthrough.
Asllani rescues Albania from the penalty spot
Albania's persistence finally paid off deep into stoppage time.
San Marino defender Filippo Fabbri was penalised for handball inside the box, with VAR confirming the decision and awarding Albania a penalty.
Asllani stepped up and converted in the 90+3rd minute, completing his brace and sending the home supporters into celebration.
Albania 2-1 San Marino
• Albania: Kristjan Asllani 11', 90+3' (pen)
• San Marino: Lorenzo Lazzari 66'
Albania strengthen their position in Group C1
The victory gives Albania nine points from four matches, with three wins and one defeat.
Albania had previously beaten Belarus 2-0 and San Marino 3-0, before losing 2-1 away to Finland on Saturday. The latest victory keeps them firmly in contention in Nations League Group C1.
Finland remain ahead of Albania after their earlier results in the group, while Belarus and San Marino occupy the other positions.
San Marino suffer another narrow defeat
For San Marino, the result represents another painful defeat after they had shown considerable resilience in Tirana.
They remain without a point in the group and had already suffered defeats against Finland, Albania and Belarus before Tuesday's encounter.
Albania, meanwhile, will take confidence from securing the victory despite being pushed all the way by their opponents.
The result leaves Maran's side with an important three points as their Nations League campaign moves towards its decisive final fixtures in November.