Leicestershire 182 for 5 (Eckersley 99*) and 143 trail Hampshire 454 for 7 dec by 129 runs
Ned Eckersley's unbeaten 99 enabled Leicestershire to keep alive their hopes of avoiding a heavy defeat by Hampshire at the Ageas Bowl.
Eckersley went to the brink of his third first-class century in an innings spread over 170 balls and which has so far including 17 boundaries as Hampshire were also frustrated by the weather.
Bad light and rain wiped 24 overs from the third day's allocation as Leicestershire fought tenaciously to reach 182 for five - still trailing by 129 - and take a one-sided match into a fourth day. Leicestershire began their second innings needing 312 to make Hampshire bat a second time and with the pitch still offering help to the pace bowlers and, later, to the spin of Danny Briggs.
Sean Ervine made the first breakthrough for Hampshire when he pinned Michael Thornely leg before wicket for 28 but it was their only success before the lunch interval.
Niall O'Brien batted almost 28 overs for his 17 before James Vince at second slip clutched a smart catch off Chris Wood and there was worse to follow for Leicestershire when their captain Ramnaresh Sarwan soon followed O'Brien to the pavilion.
Sarwan managed only three before driving James Tomlinson, who took four for 23 in the first innings, to point where Michael Carberry held the catch.
Leicestershire slumped to 95 for 4 when Joshua Cobb was held by Vince's reflex catch at short leg and only then did a minor recovery begin, inspired by Eckersley.
With Matthew Boyce as his fifth wicket partner, Eckersley dominated a stand of 64 in 26 overs and for the first time in two days in the field Hampshire were struggling to make the best of their dominance.
Briggs eventually ended the partnership when Boyce, who had made 30, drove to Wood at backward point to leave Leicestershire on 159 for five.
Shiv Thakor then supported Eckersley until the close although much depends on the pair if Hampshire are to be denied an opening-fixture victory after being on top for so long.