The victory was fraught with danger at times and probably more flattering than the home nation deserved, but three crucial qualifying points ensures the momentum continues ahead of Wednesday's meeting with France.
Goals from Kris Boyd, McManus and McFadden earned the trio national hero status, while a dubious penalty converted by Tomas Danilevicius will no doubt prompt questions when the euphoria has subsided.
Alan Hutton and Jay McEveley both made their first starts in the full-back positions, although the decision most likely to have raised eyebrows ahead of the game was the inclusion of Gary Teale on the right of midfield. There was no place for Paul Hartley or McFadden in the starting line-up.
Lithuanian coach Algimantas Liubinskas had named six Hearts players in his squad but only two started at Hampden, Deividas Cesnauskis and Andrius Velicka, plus former Dunfermline centre-half Andrius Skerla.
That 52,000 tickets were snapped up for the visit of one of the less glamorous nations in the tournament demonstrated just how far Scottish expectations have risen from a few years ago when less than half that amount would have made the journey to the national stadium.
The action on the park was far from inspirational early on. A Lithuania free-kick could have caused problems when Scott Brown was deemed to have fouled Danilevicius a few yards outside the box.
Mindaugas Kalonas was wasteful with the set-piece but was given the opportunity to make amends when the ball pinged back into his path. However, Craig Gordon was never really troubled by an effort screwed well over the crossbar.
Velicka then indulged in gamesmanship in a bid to earn the visitors a foothold in the game by going to ground twice in the box following challenges from Davie Weir.
But the Hearts man, whose antics last season saw Falkirk's Darren Barr wrongly dismissed in a league match, failed to impress the official.
The first real incident of note from Scotland arrived with 20 minutes gone and Lithuania would surely have found themselves in arrears had it not been for the heroics of their goalkeeper Zydrunas Karcemarskas.
He pulled off a superb double save to firstly prevent Boyd's header nestling in the net, before pawing a Lee McCulloch follow-up to safety. McCulloch, though, should have made more of the opportunity.
When the breakthrough came after 31 minutes, it even caught McLeish by surprise. The Scotland manager was busily scribbling in his notepad, perhaps pondering whether to tweak his system, when Boyd claimed the opener.
Darren Fletcher - who had retained the captaincy in the absence of the suspended Barry Ferguson - delivered a tantalising free-kick from the right into the box and the Rangers striker out-muscled Skerla to connect with the header, which he bulleted past Karcemarskas.
Boyd then passed up a couple of chances to double his haul before half-time. A left-footed volley prompted a one-handed save from Karcemarskas before an enticing through-ball from Fletcher saw Boyd wastefully smash his shot off the body of the onrushing goalkeeper.
Two Hearts players, Saulius Mikoliunas and Audrius Ksanavicius, were thrown into the action after the break and the Tynecastle connection intensified when former Hearts striker Edgaras Jankauskas replaced Marius Stankevicius, who was withdrawn shortly after the restart after appearing to land awkwardly on his arm.
Mikoliunas had an almost instant, and devastating, impact on the game.
Blatantly throwing himself to the ground under pressure from Fletcher, he earned an extremely dubious penalty with 59 minutes gone, deceiving 31-year-old referee Damir Skomina.
Danilevicius stepped up to convert from 12 yards to restore parity.
McFadden then bounded off the bench, replacing Teale, with the intention of restoring Scotland's lead but it was McManus who was next to threaten.
His header was saved at the keeper's right-hand post before he resumed his defensive duties at the other end by blocking a goalbound effort from Kalonas.
McManus' near-miss proved to be a preview of what was to come from the Celtic captain. McLeish went for broke by introducing Craig Beattie and Shaun Maloney.
Aston Villa man Maloney, with his first touch, lobbed Fletcher's short corner to the back post, where McManus was waiting to rifle home with 13 minutes remaining.
Any hope of a second Lithuania comeback was snuffed out seven minutes from time when McFadden's 25-yard curling left-footed drive nestled in the back of the Lithuania net.
Paris, and World Cup runners-up France, now await Scotland's challenge.