Home nerves were settled early on when Patrick Kisnorbo scored City's first goal of the season. Stephen Hughes then put the Foxes in charge before a late Matt Richards strike briefly raised Ipswich hopes, which were snuffed out by Iain Hume in time added on.
Leicester went close on four minutes when Hammond laid off a cross from Low for Hughes, whose shot forced Town keeper Shane Supple into a diving save.
Ipswich's first chance came after eight minutes but Nick Forster's angled drive lacked the venom to trouble Paul Henderson.
Relief surged through the home support on eight minutes when City took the lead with their first goal of the new campaign.
Danny Tiatto swung over a free-kick from the right and Kisnorbo rose unchallenged to direct a header home from ten yards.
Low was proving a useful conduit down City's right and after 25 minutes he floated over a quality cross which Matty Fryatt headed narrowly over.
Fryatt then squandered a chance to double his side's advantage when from close range he failed to make a clean connection with another cross from the impressive Low.
But the former Walsall hitman refused to be discouraged and was close again on 41 minutes when his tight angled shot was deflected wide by Jason De Vos.
Ipswich sought to pep up their attack with a half-time change which saw Sam Parkin replace Forster.
But it was the Foxes who scampered into a two-goal lead on 50 minutes when Dean Bowditch made a mess of Low's high, looping cross, heading in to the path of Hughes who had time and space to steer a brilliantly placed shot beyond Supple from 16 yards.
On 70 minutes Gavin WIlliams conjured up a rare threat for the visitors but Paul Henderson reacted well to turn away the midfielder's powerful drive.
Five minutes from the end Ipswich were thrown a lifeline when a half-clearance by Hughes fell to substitute Richards, whose 20-yard shot took a deflection on its way into the net.
Then, in time added on, Henderson kept his cool to hang onto a well struck free-kick from Gavin Williams.
Right at the death Hume took advantage of hesitancy in the Ipswich rearguard to score City's third, latching on to Fryatt's throughball and lifting a shot over the advancing Supple.