The Seagulls were not at their best against the Tractor Boys but Craig Mackail-Smith's first-half strike and a double from Barnes after the interval wrapped up a comfortable victory.
Brighton have not been defeated in the league since December 31 and they moved up to seventh, level on points with Cardiff, who occupy the final play-off place.
After weathering an early assault on their goal from Ipswich, Mackail-Smith broke the deadlock with a close-range finish.
Ipswich striker Michael Chopra had a goal disallowed for handball but Barnes' fantastic 25-yard strike doubled Brighton's lead before the striker wrapped up the points late on.
Paul Jewell's men had won their four previous matches before their trip to the south coast and had kept successive clean sheets in their last two but they were poor for large spells this afternoon.
Ipswich started brightly as they sought to continue their winning streak, with midfielder Jay Emmanuel-Thomas' long-range effort forcing an early save from Peter Brezovan.
A stray back pass from Joe Mattock put Albion's goalkeeper under unnecessary pressure and although his clearance was intercepted, Chopra's chip was cleared off the line by Gordon Greer.
It proved to be a vital interception by the defender, who then played a key part as Mackail-Smith broke the deadlock for Brighton in the 20th minute.
Greer's pass from deep in his own half split Town's defence before Will Buckley's first-time low cross from the right allowed Mackail-Smith to slot home from close in.
Buoyed by his strike, the former Peterborough striker nearly doubled his tally but after getting away from his marker, he could only head against the crossbar from Buckley's corner.
Ipswich were firmly on the back foot after conceding but Lee Martin's strike from 25 yards was parried away by a scrambling Brezovan shortly before the interval.
Chopra thought he had levelled proceedings at the start of the second half after turning and firing past Brezovan but the striker was penalised for bringing down Martin's corner with his hand.
Ipswich continued to push forward in search of an equaliser but their failure to create another meaningful opportunity came back to haunt them as Barnes doubled Brighton's lead in the 65th minute.
A poor clearance from Town keeper Arran Lee-Barrett was collected by Liam Bridcutt and he picked out Barnes, who cut in from the left and curled wonderfully past Lee-Barrett from 25 yards for his 10th goal of the season.
Carlos Edwards could have set up a tense finale but his strike from six yards was well blocked by Brighton defender Adam El-Abd.
And Barnes ensured there would be no way back for the visitors with a low finish from Gonzalo Jara Reyes' right-wing cross in the 88th minute.