The Championship side converted all four of their spot kicks in the shoot out with Shrewsbury's Jake Robinson seeing his penalty saved by Shane Supple before skipper Graham Coughlan hammered his kick over the bar.
The result vindicated Keane's decision to make ten changes from the side beaten at Coventry on Sunday with the host of youngsters drafted in justifying the faith shown in them.
Ipswich drew first blood in the 12th minute as exciting teenage striker Connor Wickham celebrated his call up to the England under-17 squad in style, turning Coughlan before driving in a low shot on the turn.
Any fears Shrewsbury 's heads would go down were soon dispelled as a flowing move resulted in a swift equaliser, Robinson slamming home Kevin McIntyre's left-wing cross for his second goal in as many games since his summer switch from Brighton .
Even better was to come for the underdogs in the 25th minute when rejuvenated striker Dave Hibbert latched on to a loose clearance from Tommy Smith and set himself up to hammer a wonderful 30 yard volley over stranded keeper Supple to the top corner of the net.
Ipswich refused to panic, though, and were quickly back on terms as Alan Quinn, one of three Irish internationals in the Ipswich side, drove a low free kick from the edge of the area beyond the reach of Chris Neal to make it 2-2 at the break.
The entertainment continued after the restart with another fine strike from Wickham restoring Ipswich's advantage before Shrewsbury deservedly forced extra time 16 minutes from time, Aussie Shane Cansdell-Sherriff crashing in a thunderous low volley from the edge of the box.
Both sides had chances to win it in extra time but it eventually all came down to the drama of penalties with Ipswich coming out on top.