Wright's 5-80 eclipsed his previous best Championship figures of 3-33
Spinner Gary Keedy took three key second-innings wickets as Lancashire wrestled control against Sussex.
Keedy removed Murray Goodwin, Matt Prior and Ed Joyce, with the day's last ball, to leave Sussex reeling on 148-5 in their second innings, a lead of 138.
Earlier, Luke Wright had sparked a fightback by Sussex by claiming his maiden first-class five-wicket haul.
His efforts helped dismiss Lancashire, for whom Mark Chilton top-scored with 89, for 299 after resuming on 209-4.
Lancashire looked set for a big total when they reached 253-5, but Wright claimed three wickets with the second new ball to finish with 5-80.
He was ably supported by Robin Martin-Jenkins, who finished with figures of 3-50 as the visitors were restricted to a 10-run first innings lead.
James Anderson soon made inroads into Sussex's second innings after changing ends, inducing Chris Nash to nibble at an away swinger before getting Michael Yardy to play on to his own stumps as he attempted to shoulder arms.
That meant the first 22 wickets in the game had all fallen to pace, but that changed when Keedy ended a third-wicket stand of 50 between Joyce and Goodwin when he had the former Zimbabwe Test batsman smartly stumped by Luke Sutton.
Prior followed two balls later, and after Joyce and Wright (35 not out) had added a further 53 for the fifth wicket, Keedy trapped Joyce lbw for 55 with the final ball of the day.
BBC Sport's John Lees reviews day three at Hove:
"What a tremendous finish is in prospect in a game in which the first 22 wickets fell to pace and the last three were claimed by the slow left-arm of Gary Keedy to leave Sussex's hopes of securing a draw very much in the balance.
"Keedy, who only bowled five overs in the first innings, claimed the prize wicket of Murray Goodwin, having him stumped by Luke Sutton, and two balls later sent back England wicketkeeper Matt Prior lbw.
"Then, with the final ball of the day, he got Ed Joyce, who had made 90 in the first innings, leg before for 55.
"Sussex went to stumps on 148-5, leading by just 138.
"At the start of the day Lancashire had resumed on 209-4 but they lost Steven Croft for 59 without the addition of a run. Mark Chilton was 72 overnight and having batted very slowly throughout the morning, departed for 89.
"The chief wicket-taker was Luke Wright, who took five wickets in an innings for the first time in first-class cricket to end with 5-80.
"It meant Lancashire were out one run short of scoring a third batting point and were only 10 runs to the good.
"That was less than Sussex seemingly feared when out for 289 on the first evening.
"James Anderson bowled at his best at the start of Sussex's second innings, claiming the wickets of Chris Nash and Michael Yardy to give him eight wickets in the game.
"Then it was the turn of Keedy to really upset the Sussex applecart.
"They will need to bat until at least lunch time on the final day to secure a draw but at the moment Lancashire are favourites to get the win."
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