Craig Brown's side gave an unconvincing performance at the sparsely- populated Ta'Qali stadium against a side who have been treated dismissively by all-comers in their own qualifying campaign and finished the match with 10 men.
Jackson scored the winner in the 81st minute, taking his tally to three goals in 19 appearances, and a minute later Malta had their substitute Noel Turner sent off for a bad foul on John Collins.
Scotland went ahead twice, through Christian Dailly, from Gary McAllister's fourth-minute free-kick, and Jackson, who tapped in on the stroke of half- time after Kevin Gallacher flicked on Tom Boyd's cross. But they were pegged back first by Hubert Suda and then by his half-time substitute, Stefan Sultana.
The quality of defending, against a side that has managed only one goal, scored by Sultana, in its World Cup group six campaign, presents a particular worry for Brown, who saw his side lose at home to Wales on Tuesday.
His initial plan for coping with the absence from the defence of the two Colins, Hendry and Calderwood, did not work, so Wimbledon's Brian McAllister was substituted at half-time. Now David Weir, of Hearts, may partner Dailly and Tom Boyd in Minsk.
"It is a paradox but I think we will benefit from our mistakes," Brown said. "We've tried three different formations in two games with Brian McAllister, David Weir and Dailly coming in with Tom Boyd. We don't have a lot of other options. We know we will have to defend better in Belarus to win."
One benefit to Brown was the promising debut in midfield by Crystal Palace's David Hopkin.
MALTA: Muscat; Attard (Turner 53), Chetcuti, Vella (Giglio, 75), Debono, Zammit, Gilbert, Saliba, Suda (Sultana, 45), Brincat, Carabott.
SCOTLAND (3-5-2): Leighton (Hibernian); Boyd (Celtic), Dailly (Derby), B McAllister (Wimbledon); Burley (Chelsea), Hopkin (Crystal Palace), G McAllister (Coventry), Collins (Monaco), T McKinlay (Celtic); Jackson (Hibernian), Gallacher (Blackburn Rovers). Substitutes: Weir (Hearts) for B McAllister, h-t; Durie (Rangers) for Gallacher, 56; Gemmill (Nottm Forest) for Hopkin, 56; Donnelly (Celtic) for Collins, 84.
Referee: S Braschi (It).