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 the 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.
Source: PA
Source: PA