Many of the near 3,000 visiting fans therefore vented their disapproval towards the Scottish Football Association board, even after Johnny Russell doubled the lead in the 74th minute.
Skipper Andy Robertson admitted on the eve of the match that Scotland could only make a small start to atoning for Thursday's 3-0 loss but they barely did that.
The opening defeat looked even worse when Group I rivals Russia won 4-0 in Kazakhstan before kick-off in San Marino and ending the first two games against the two lowest-ranked teams on minus goal difference is a major setback, especially given Cyprus put five past San Marino.
The omens for a resounding win were not good. Scotland had only won 2-0 on each of their three visits to San Marino, twice on their way to reaching the European Championship finals in the 1990s.
McLeish made six changes and a bold choice in his central striking role in Cardiff's Callum Paterson – a midfielder for his club and a right-back for his country in the November wins over Albania and Israel.
Paterson and Bournemouth wide player Ryan Fraser were back in after being allowed to miss the opening qualifier under an agreement with their clubs over concerns about the artificial surface, while Robertson returned after dental surgery.
Right-back Stephen O'Donnell also came in along with Russell and McLean, with James Forrest among the players dropped.
Scotland started with verve and McLean came close with a fierce 20-yard volley before glancing home Fraser's cross and settling the nerves.
But there was no lift-off as the tempo gradually tailed off. Russell was twice off target with half-chances before teeing up Stuart Armstrong in the 20th minute but Ella Benedettini produced an impressive double stop.
Slackness remained evident in the visitors' play and there was a scare on the half-hour mark when Jose Hirsch got in between Scotland's centre-backs and went round Scott Bain, but he shot into the side netting from a difficult angle.
Paterson went off injured after landing awkwardly as he had a header theatrically saved and Marc McNulty eventually took his place.
There was a lack of quality about Scotland's final ball, evidenced by Russell and Fraser wasting free-kicks and the latter crossing straight out of the park, before the half-time whistle was met by a few boos.
There was another scare just after the restart when Filippo Berardi went down in the box under the close attention of Scott McKenna but the referee was unimpressed.
McNulty had a shot deflected wide and McKenna glanced a header just past but Scotland were labouring and the introduction of Scott McTominay for Callum McGregor did little to change things.
Forrest replaced Armstrong in the 71st minute and soon set up Russell on the break to net from close range, with McNulty assisting matters by setting the Celtic winger free and leaving his low cross.
McNulty had good chances to add to the lead but headed Forrest's cross wide from six yards and then saw his attempted lob diverted over.
The final whistle was met with a few jeers but more applause from the travelling fans.