When the goal finally came it was surrounded in controversy with Crewe convinced referee Andy Hall had made the wrong decision after ruling that David Wright had illegally hauled down Jordan Stewart inside the box.
It looked like a harsh decision but after the protests had subsided the Scottish international kept his nerve to calmly slot home the spot kick.
City began the game keen to rekindle the glory days of the Martin O'Neill era in which they reached three Finals in this competition, lifting the trophy twice.
Leicester enjoyed plenty of early possession, but Brian Deane should have given them a 12th minute lead when a Lilian Nalis cross fell to him eight yards out.
No-one was more disappointed than Deane who fired over with only the keeper to beat.
Crewe then showed that they were not playing just to make up the numbers and gave the East Midlanders a scare on 19 minutes when Justin Cochrane's looping header seemed destined for the top corner until Ian Walker intervened with an acrobatic save to palm the ball out for a corner.
Nalis hit back for City with a trademark 25-yard volley which had keeper Clayton Ince at full stretch.
At the other end Leicester again had a narrow escape when Paul Edwards lifted the ball over a hesitant Walker but Steve Howey got back in time to head the ball off the line.
Leicester boss Micky Adams threw on substitute Muzzy Izzet for James Scowcroft for the second half in a bid to inject more creativity in his misfiring side.
But City continued to labour and were given another wake-up call on the hour mark when Edwards nodded a Wright cross just wide of the frame.
That scare signalled a long period of domination by the Foxes but they continued to struggle in their efforts to find a way through Crewe's well-drilled defence.
Dickov, however, went close on 78 minutes when he arrowed a 25-yard drive towards the top corner of the Crewe goal but Ince was again at full stretch to tip the ball over the bar.
With the game drifting towards extra time City finally broke through on 80 minutes when referee Andy Hall ruled that Wright had illegally hauled down Stewart inside the area.
Leicester: Walker, Curtis, Sinclair, Howey, Impey, Brooker, Nalis, Scimeca, Scowcroft, Dickov, Deane. Subs: Coyne, Izzet, Stewart, McKinlay, Priet.
Crewe: Ince, Wright, Walker, Foster, Vaughan, Lunt, Brammer, Cochrane, Rix, Ashton, Edwards. Subs: Tonkin, Sorvel, McCready, Varney, Bankole.
Referee: A Hall (West Midlands).