Sir Bobby Robson's team, including Burley at right-back, chalked up 15 straight home wins during the 1980-81 season and Jim Magilton's modern-day team have now achieved 12.
This one was fairly routine in a poor game, with both Town goals owing a fair bit to good fortune, as Billy Clarke's shot deflected in off Jon Walters and Pablo Counago scored with a deflected header.
The visitors offered little, although Neil Alexander made a fine save at 1-0 to tip a Bradley Wright-Phillips volley over the bar, and promising youngster Adam Hammill was unlucky with a chip which came back off the post.
The first half took an age to get going, but finally picked up as both Counago and Clarke fired over from distance for Tow, and both Wright-Phillips and Hammill were off-target for Saints.
Town came close on the half hour when Counago's low cross almost found Alan Lee, only for Saints to scramble it away, but the hosts then went in front on 34 minutes.
Tommy Miller tapped a free-kick sideways and Clarke fired in a firm shot which looked to be going well wide, but it struck the heels of Walters and spun across goal and out of the reach of Kelvin Davis.
The second half had to be better and thankfully it was with Southampton going close two minutes in when Phil Ifil crossed to find Wright-Phillips, whose volley from six yards was touched over the bar by Alexander.
Both sides then hit the woodwork in the space of three minutes as first Owen Garvan shot against the bar when a Tommy Miller corner fell to him, and then Hammill chipped Alexander, but hit the far post from a Wright-Phillips pass.
Ifil did well to stop Walters streaking onto a clever Counago backheel, before Alexander dived to hold a 25-yarder from Jason Euell low down by his right-hand post.
Ipswich were close to a second on 58 minutes when Miller robbed the dawdling Rudi Skacel on the edge of his own box and fed Counago, whose low shot was creeping into the corner but Davis pulled off a fine diving save.
A fine Counago pass sent Walters clear, but his low drive flashed across the face of goal with Alan Lee just unable to slide in and apply the finish, before Stern John headed wide from a Hammill cross.
Counago made it 2-0 on 69 minutes when Miller whipped a dangerous free-kick into the six-yard box and the Spaniard's back header was deflected in beyond the helpless Davis.
After that there was little action at either end as a spate of substitutions broke up the flow of the game, although Alexander saved a firm Andrew Davies header and also scrambled away a driven cross-cum-shot from Wright-Phillips.