The on-loan Sunderland striker netted his fourth and fifth goals for the club to seal all three points for Ipswich, who extended their unbeaten run at home to 12 matches and moved four points clear of the bottom three.
But sixth-placed Cardiff, who are due in the High Court on Wednesday to face a winding-up order over money owed to HM Revenue and Customs, lacked ideas in attack and wasted the chance to leapfrog Leicester into fifth place in the Championship.
Ipswich came close to breaking the deadlock after just eight minutes when Owen Garvan's cross was met by the head of Murphy, but Cardiff goalkeeper David Marshall stretched to his left to superbly tip the ball behind for a corner.
At the other end, Michael Chopra, who last scored a league goal in the 2-1 win over Doncaster on January 30, tried his luck with an overhead kick soon after but it sailed just over the crossbar.
Ipswich striker David Healy tried to impose himself on the game but his first effort of the game was blocked by defender Gabor Gyepes before the on-loan Sunderland man hit a tame long-range shot straight at Marshall.
But Town made no mistake next time around as Jack Colback picked out Murphy with a superb pass and the striker was on hand to fire home - his first in five games - from close range after 18 minutes.
Promotion-chasing Cardiff failed to impose themselves on the game and would have been two goals down had it not been for the heroics of Marshall.
Gareth McAuley latched onto Garvan's cross and his right-footed effort had Marshall at full stretch, but the Bluebirds goalkeeper managed to tip the ball round a post for a corner.
Cardiff should have levelled in the closing minutes of the half when Chopra was given time and space in the penalty area, but the striker mishit his effort wide of the left post.
Midfielder Shane O'Connor, who was making his home debut, impressed in midfield for Ipswich as the hosts held on to their more than deserved lead going in at the break.
Cardiff wasted an opportunity to level the scores within four minutes of the restart as Chopra sent his long-range effort wide of the mark.
Anthony Gerrard also tried his luck from distance but the defender failed to trouble Brian Murphy in the Ipswich goal.
And the Bluebirds' wasteful finishing proved costly as Roy Keane's men doubled their advantage after 58 minutes.
Garvan's initial effort was excellently touched away by Marshall, but Murphy was on hand to net the rebound.
Murphy almost grabbed his first hat-trick in Ipswich colours after 66 minutes but his right-footed effort was superbly kept out by Marshall, who produced another fine save to deny Pablo Counago soon after, as Ipswich held on for an easy win.