All-rounder James Coles produced a career-best 59 as the Sussex batters put on a mammoth 588 runs in their first innings before the away side dug in to fight back on and a well-contested second day of County Cricket.
Leicestershire produced an impressive response after Steven Finn dismissed opener Hassan Azad with the opening delivery of the second innings.
Rishi Patel and Louis Kimber then batted with increasing authority in an unbroken stand which took them to 159 for one at stumps, to leave them trailing by 429.
Earlier, Sussex had piled up their highest total for seven years, after Ollie Carter, Delray Rawlins and James Coles, the 18-year-old making only his fifth first-class appearance, all scored half-centuries.
Resuming on 407-4, Carter and Rawlins extended their fifth-wicket stand to 119 in 25 overs.
Parkinson came into the attack in the 18th over of the day and Rawlins hit his first ball for four to bring up his half-century.
But Parkinson struck in his next over when Carter played on for 75 attempting to dab the ball into the off side. It was another fine innings by the in-form 20-year-old, who has scored 422 runs in his last five Championship innings.
Rawlins was another that batted brilliantly for Sussex making 75 from 115 balls to prolong the time the Leicestershire fielders had to spend out in the middle once again.
Coles added 49 for the last wicket with Sean Hunt, hitting four sixes in his 59 in his maiden first-class fifty before he was beaten in the flight by Parkinson coming down the pitch once more.
Parkinson’s hard graft was rewarded with figures of five for 128 from 41.5 overs while 61 extras swelled the Sussex total.
Steve Finn, captaining Sussex after Tom Haines broke his hand on Monday, made an immediate impact when Azad was caught at slip off a ball which did just enough off the seam to take the edge.
But Patel and Kimber got their heads down to negotiate the new ball although they both offered half-chances.
Once the new ball lost its hardness, though, batting became much more straightforward and at stumps Kimber was in sight of his maiden first-class hundred, having already reached a career-best 91 while Patel passed fifty for the third time in his career.