Spurs dominated large sections of the game at Cardiff City Stadium but were denied on countless occasions as the Scot made crucial saves from Roberto Soldado, Christian Eriksen, Paulinho and Gylfi Sigurdsson.
Even when former Swansea man Sigurdsson did beat Marshall his effort struck the crossbar, but Paulinho finally made their dominance tell as he tapped in Erik Lamela's pass from close range to seal a 1-0 win.
Cardiff created few clear chances but felt they had twice come out on the wrong end of decisions by the officials.
The first came when Hugo Lloris appeared to handle outside his area as Fraizer Campbell attempted to round him, although replays suggested it was a very tight call.
The second saw Ben Turner's header from a corner chalked off after Aron Gunnarsson was adjudged to have impeded Lloris.
Although Spurs would take a stranglehold on proceedings, Cardiff made a purposeful opening, with Kevin Theophile-Catherine heavily involved on his home debut.
The Bluebirds should have led in the seventh minute. Kyle Naughton's misdirected pass was left by Michael Dawson, but lacked the weight to get back to Lloris.
Campbell pounced but he was robbed of the ball as he attempted to round Lloris on the edge of the box, with replays suggesting the Frenchman had handled outside his area.
Spurs boss Andre Villas-Boas had bemoaned his side's run of three games in six days earlier this week, but he need not have worried about their ability to perform, as they settled down and assumed control.
They crafted a fine chance for Soldado, after a thrilling burst from Andros Townsend, but Marshall was able to turn the Spaniard's shot round the post.
Kyle Walker followed the winger's lead as he took off from inside his own half on a run that took him into the Cardiff box, where Ben Turner made a crucial tackle.
Marshall soon found himself severely overworked saving twice from Eriksen, the second coming after Turner had recovered from being horribly exposed by Soldado to get a block in.
Sigurdsson also stung the Scotland keeper's palms, but Cardiff then enjoyed a better spell up to half-time, and they were aggrieved not to be leading at the break.
Lloris' poor control of a backpass gifted Cardiff a corner, which Turner headed in at the far post, but referee Mark Clattenburg ruled the keeper had been impeded by Gunnarsson. It appeared a soft decision.
Cardiff's gradual improvement continued at the start of the second half, with Craig Bellamy racing clear only for Lloris to cut out his pull-back for Peter Whittingham.
But the hosts were again indebted to Marshall moments later. Sigurdsson's shot from the edge of the box came back off the crossbar to fall to Soldado in acres of space, but he was again denied by the keeper's legs.
Sigurdsson was involved once more when he scampered round Theophile-Catherine to tee up Paulinho, but again Marshall was up to the task.
Cardiff boss Malky Mackay threw on Peter Odemwingie in place of Campbell for his debut, and the Nigerian almost enjoyed a dream start as he curled wide of the left-hand upright.
It proved a brief respite as Spurs continued to pile on the pressure, but Cardiff held firm as the game entered the final 15 minutes.
The hosts spurned a great chance to win it as Odemwingie evaded Jan Vertonghen and pulled back for Gunnarsson, who fired high over the crossbar.
Marshall saved from Paulinho at the other end, but could do nothing to keep out the Brazilian's final effort from inside the six-yard box.
Source: PA
Source: PA