Brendan Rodgers' side, up to fourth following Monday's results, cannot now be caught by those outside the top six, although the second automatic spot is all but beyond them with just two matches remaining.
On-loan Chelsea forward Fabio Borini broke the deadlock at the Liberty Stadium after just nine minutes and it was soon 2-0 courtesy of Luke Moore's strike, which owed much to the failures of Town goalkeeper Arran Lee-Barrett.
Ipswich, missing star names Connor Wickham and Jimmy Bullard due to rib and shoulder injuries respectively, were largely ineffective but did gain brief hope courtesy of recalled Colin Healy's second goal in a Town shirt.
But Borini, with the fourth goal of the first half, soon restored City's two-goal advantage from close range to make it six goals in eight Swans starts.
Substitute Scott Sinclair then added a penalty during what was a largely lifeless second period to ensure Ipswich, who lost 5-1 at home to neighbours Norwich on Thursday, shipped nine goals over the Easter period.
Swansea, with just one day's full rest since their last outing compared to Ipswich's three, showed four changes - Moore, Joe Allen, Stephen Dobbie and Neil Taylor coming in.
And, after Dorus de Vries made a good early save from David Norris, it was the hosts who broke the deadlock early on courtesy of Borini.
The highly-rated Chelsea man superbly finished off what was a patient, well-worked move down the right channel, stroking a right-footed shot from 12 yards into the bottom corner.
Swans were firmly on the offensive and five minutes later and it was 2-0, with huge question marks hanging over Lee-Barrett.
Moore let fly with a 20-yard strike which did not appear to take a deflection but may have moved in the air as the Town keeper, who went to his right, was beaten straight down the middle.
Yet, in a pulsating start to the afternoon, Ipswich were straight back in it as former Swans striker Jason Scotland laid the ball back to Healy and he hit a sweet strike into the top corner from the edge of the penalty area.
The clash temporarily appeared finely poised but it was not long before the Swans regained their two-goal advantage.
The lively Nathan Dyer sent Moore clean through, his shot was parried by Lee-Barrett and Borini was on hand to poke home from less than a yard out.
Swans boss Brendan Rodgers replaced Borini at the break due to a suspected injury although Sinclair, with 17 league goals to his name before today, was a more than able replacement.
Town counterpart Paul Jewell also lost Darren O'Dea and Gareth McAuley to injury.
The second half was in complete contrast to the first, with a definite end-of-season feel to it and chances at a minimum.
Mark Kennedy's 70th-minute foul on Leon Britton brought the 16,001 present back to life, with Sinclair converting the resulting penalty.
And all Swansea eyes will now be on ending the season brightly ahead of their forthcoming play-off quest for Barclays Premier League football.