But, as Ipswich probed for a route back into the affair, Saints strengthened their grip with a third minutes before half-time.
Lallana broke and found Guly, the Brazilian rounded David Stockdale and found space to square the ball for Connolly to fire home from close range.
Jewell brought on Emmanuel-Thomas and Lee Martin at the break and the changes certainly had a positive effect.
It was Andrews, on loan from Blackburn, who grabbed a lifeline in the 56th minute, following up well after Michael Chopra's stunning strike had rebounded off the crossbar.
Cresswell made a crucial goal-line clearance from Lallana which would have swung the game back in Saints' favour.
And no sooner had the hosts made vital contributions at both ends as they made it 3-2 as Emmanuel-Thomas converted from close range.
But Lallana ended the comeback in the 76th minute when he latched onto Morgan Schneiderlin's through-ball to convert past Stockdale.
And there was still time for a late fifth as the midfielder used his pace to confirm a third home defeat in a week for the Tractor Boys.
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