Marshall made his first excellent save on nine minutes when he brilliantly palmed away Murphy's goalbound header from Owen Garvan's cross, while soon after Michael Chopra sent an overhead kick narrowly over for the visitors.
Town went ahead on 18 minutes when David Healy hooked a high ball into the box which Jack Colback brought down superbly, before he laid it off to Murphy whose first-time shot found the corner with Marshall unsighted.
Colback shot over from 20 yards and after a quiet spell in the game Town went close again when a loose ball dropped to Gareth McAuley following a Garvan corner and the defender's toe-poke goalwards forced a diving save from Marshall.
Darcy Blake volleyed over from an Adam Matthews long throw before Marshall made a more routine save from another Murphy header, this time after he was found by Jon Walters.
Chopra had a good chance just before the interval when Jay Bothroyd flicked on a Kevin McNaughton cross, but the striker's first touch was poor and with his second he blazed over.
Chopra shot over from another Bothroyd lay-off after the break, but was then lucky to stay on after appearing to stamp on Garvan and then clip him around the back of the head, but referee Grant Hegley only issued a yellow card.
Garvan had the last laugh a couple of minutes later when he fired in a 25-yard screamer which Marshall brilliantly parried, but it went straight into the path of Murphy who swept the loose ball home.
Cardiff finally got an effort on target on the hour through a 20-yard snap-shot from Bothroyd, but Brian Murphy saved with ease and then Gavin Rae volleyed over from a long throw by Tony Capaldi as the Bluebirds tried to rally.
Marshall got lucky when he fired a clearance against Walters but was able to get to the loose ball first before he produced another stunning save when David Wright's shot was deflected into the path of Murphy who connected well, only for Marshall to tip his effort against the bar and over.
Marshall produced two more excellent saves as first he tipped over a close-range header from sub Pablo Counago following a Walters cross, then made a reflex stop when Bothroyd directed a Damien Delaney cross towards his own net.
Murphy departed to a standing ovation with ten minutes remaining and although Ipswich have been edgy at times seeing out games in which they have had the lead late on, they made no mistake this time.
Cardiff pumped several balls into the box from decent positions, but nothing got past the outstanding McAuley and Delaney, while Town threatened several times on the break, without quite finding the killer pass.