Palace boss Sam Allardyce recently admitted he hopes Zaha puts pen to paper on a new contract if the Eagles avoid relegation this season.
Southampton climbed from 13th to ninth place.
"Nobody really knows me apart from the players and the staff here, what I'm really like on a day to day basis because they see me when I walk through the door and when I'm behind the scenes in the dressing room".
Palace have three games in six days at the end of the month and Allardyce is desperate for his injured players, including Patrick van Aanholt, James Tomkins, Pape Souare, Yohan Cabaye, Connor Wickham, Loic Remy and Fraizer Campbell, to recover.
The troublesome penalty spot, where Bournemouth's Harry Arter spectacularly missed on Saturday, was relaid with a patch of hybrid turf to ensure the surface was 100% firm from 12 yards.
Long was Southampton's biggest culprit in front of goal, thrice guilty of missing from close range.
Germany approves bill to target hate crime, fake news
But a local tech lobby group, Bitkom, is concerned that social media platforms will feel compelled to err in favour of censorship. Mass also said that there would need to be similar laws implemented across the European Union for the crackdown to truly work.
Palace were jubilant while Southampton raged.
After having what appeared to be a certain penalty waved away by referee Roger East, Southampton deservedly drew level just prior to the interval through Nathan Redmond's strike.
Wayne Hennessey saved well from Redmond's tidy header, but midway through the first half, Palace were on the rise.
Mauricio Pochettino will be keen on bolstering his attacking options this summer as he looks for more regular sources for goals beyond Harry Kane, and Zaha will certainly add a new dynamic to the team while offering competition for the likes of Christian Eriksen and Heung-Min Son. The Palace defender nearly punched clear as Dusan Tadic tried to create space in the visitors' box.
Sakho denied Davis a definite goal, before the Saints captain's follow-up was blocked by Damien Delaney. But eventually Crystal Palace's defence gave way, with the unlikely hero Yoshida as he tapped home at the back post from Redmond's cross.
Suddenly Saints shook the shackles, with Ward-Prowse firing the third after good approach play from Tadic and Soares.