Left-arm spinner Simon Kerrigan continued his good start to the season with five for 70 and despite Tom Haines’ second hundred of the season Sussex were bowled out for 298 in their second innings.
That left Northants more than four sessions to score 218 and they were 131 for two at stumps on day three, needing another 87.
Haines made an excellent 103 – the first Championship hundred by a Sussex player at Hove for two years – and Ben Brown was last out for 95 trying to hit a six to get to his century.
Sussex had resumed on 142 for four and Haines and Brown took their fifth-wicket stand to 103 but shortly after reaching the fourth hundred of his career, Haines turned a ball from Kerrigan to mid-wicket. It was a somewhat tame end to a fine innings by the 22-year-old left-hander, who faced 221 balls and hit 11 fours.
Tom Taylor picked up two wickets in successive balls with Delray Rawlins (15) bowled aiming a big drive and George Garton edging low to first slip.
But Jack Carson, fresh from his maiden first-class fifty in the first innings, gave Brown admirable support either side of lunch in an eighth-wicket stand of 65 which took the score to 297.
The luckless Ben Sanderson could not break through with the second new ball but Kerrigan came to the rescue. Carson was pinned in front playing back for 35 before Taylor yorked Henry Crocombe in the next over for a duck.
That left Brown on 95 with only last man Jamie Atkins for company and he went for glory, only to be caught on the long-off boundary. The Sussex captain faced 170 balls and hit ten fours.
Although the odd ball did turn, the pitch had got easier to bat on. Sussex needed early wickets and Atkins got them a breakthrough in his first over when Ben Curran (10), whose nine innings this season have brought only 141 runs, was caught behind aiming an expansive drive.
Vasconcelos and Luke Procter took the score to 57 with few alarms before Haines enjoyed his second memorable moment of the day, running round from mid-wicket to run out Vasconcelos (38) with a brilliant direct hit.
But Luke Procter (47 not out) and Rob Keogh (23 not out) settled the nerves with an unbroken third-wicket stand of 73 to put their side in sight of victory.
Sussex batsman Tom Haines said: “That hundred against a quality bowling attack felt really special and as you could tell by my celebrations it was a bit of a relief as well. It has felt different this week having supporters back and to have every run clapped definitely helped my performance, I’m really pleased. It will need something special for us to win but wickets tend to fall in numbers in the morning session at Hove – stranger things have happened.”