At 114 for 4, Northamptonshire were sorely threatened with following on, but Curran and Tony Penberthy averted it by sharing an unbroken partnership of 187.
Zimbabweans are noted for a forthright batting approach - as Leicestershire knew after Brian Davison's past flamboyance for them. Curran took a few risks, Penberthy followed his doctrines, and Leicestershire were doomed to frustration as chances flew just out of reach, and Paul Nixon missed an easy stumping chance presented by Penberthy, on 33.
Moderate bowling compounded Leicestershire's difficulties. Alan Mullally, watched by the England chairman, Ray Illingworth,was wayward and wicketless, his first 19 overs costing 59 runs.
Three bowling changes yielded first-over wickets for Vince Wells, Matthew Brimson and Phil Simmons - but Leicestershire missed the injured David Millns in a match of multiple absentees.
Northamptonshire needed Curran's unbeaten century, with 16 fours from 149 balls, after Alan Fordham, the acting captain, and potential major innings player was dismissed by Brimson's arm ball. Mal Loye edged a low catch to Nixon and David Capel was caught at first slip from Simmons' third delivery.
Mullally fired a few rockets at Curran late in the day but, for Leicestershire, it was damage limitation on a pitch showing signs of turn.
Adrian Pierson induced enough to prompt Penberthy, on 49, to edge a sharp but fumbled catch to Simmons, as fortune favoured the brave in the most substantial partnership of the match.
Northamptonshire still face the prospect of batting last, hardly a happy prospect given the ground's track record this summer. In the previous game, Sussex, in search of 213 to win, lost by 58 runs, providing Leicestershire with their fourth consecutive championship victory.
Another had already looked on the way when Leicestershire headed beyond 400, courtesy of Mullally, who struck four remarkable and consecutive boundaries off Curtly Ambrose.
Wells had departed in the morning's third over, chipping a slower ball from Capel to mid-on. His innings of 204 included 30 fours and a six, from 303 balls. To win this game, Leicestershire need a swift breakthrough today to reach the soft underbelly of Northamptonshire's lower- order batting.Reuse content