The victory helped Roy Keane's men edge closer to Championship safety, while damaging Barnsley's slender play-off hopes.
Murphy netted after just four minutes as Town dominated early on, but Barnsley had more of the pressure after the break, but couldn't break down a home defence which has now kept four clean sheets in a row at Portman Road.
Ipswich started brightly with Carlos Edwards firing over after a neat Pablo Counago lay-off and the Spaniard then sent Murphy clear only to be denied by a great tackle by Ryan Shotton.
The pressure told though when Counago chased a hopeful punt downfield and robbed dithering goalkeeper Luke Steele as he tried to let the ball run out for a throw. His shot from a narrow angle then rebounded off the post and straight to Murphy who couldn't miss.
Town continued to threaten and Counago next fed Jack Colback whose fierce 20-yarder flew wide and Counago himself then tamely dragged his shot wide after Murphy had laid off Shane O'Connor's cross.
Still Barnsley couldn't gain a foothold in the game and Steele next had to make a good diving save to turn away Gareth McAuley's header across goal before Jon Walters cut in off the left wing and curled his 20-yarder just wide.
Colback was fortunate to escape with just a yellow card after a wild lunge on Bobby Hassell before Edwards fired well over again for the hosts.
Barnsley were having slightly more of the ball, but it was Town that continued to carry the greater threat and Steele got down smartly to turn away a driven low cross from Damien Delaney before it was hacked clear.
Town began the second half in sloppy fashion and Barnsley accepted the invitation to get into the game at last as Nathan Doyle screwed a 20-yard effort wide and Stephen Foster then fired over from an angle following a free-kick.
Delaney then did well to deflect a Hugo Colace shot over the bar and, after 56 minutes, Keane had seen enough and sent on Jaime Peters and Connor Wickham for Edwards and Counago respectively.
Within two minutes Wickham had the ball in the net after a run and cross to the far post by Peters but the 16-year-old, who had scored the winner the previous weekend against Scunthorpe, had strayed offside.
David Norris shot tamely at Steele after a neat one-two with Murphy before McAuley did well to clear a dangerous low cross from Daniel Bogdanovic ahead of former Ipswich loanee Jon Macken, who scored the winner in this fixture at Oakwell.
Emil Halfredsson dragged a decent chance wide before sub Iain Hume saw his effort blocked by Delaney and fellow replacement Reuben Noble-Lazarus shot tamely at Brian Murphy with the follow-up.
Ipswich switched to just one up front for the final ten minutes, which was nearer to 15 with the added time, and they had a few nervy moments as Bogdanovic headed over and Colace forced a save from Brian Murphy, but the hosts held on relatively comfortably to reach their highest League position of the season, 15th.