Former Worthing skipper Mark Burt scored a debut goal as Southwick made it six points out of six with a 1-0 win at home to Peacehaven.
Burt, who signed for Wickers on Saturday, scrambled home the only goal of the contest 12 minutes from time.
Winning boss Sammy Donnelly said: "The encouraging thing is that once again we kept a clean sheet. Keeping clean sheets gives you something to build on."
Like Southwick, Three Bridges and Chichester also have maximum points after two games.
Bridges had opened with a 6-2 win over Wick on Saturday but they needed a last minute Scott Langridge goal to beat Shoreham 3-2 last night.
Shoreham twice led through Dicker and Pulling but Bridges drew level thanks to Justin Henderson and a Pat Massaro penalty before Massaro delivered a last minute corner which Langridge powerfully headed into the net.
Manager Micky Taylor said: "It is all right to play pretty football and score six goals but sometimes you have to dig in and show character. This was more pleasing than Saturday."
Neil Murfin scored twice with Roger Moore adding a last minute third as Chichester won 3-1 at home to Arundel. Gary Norgate netted his second in as many games for the visitors.
Matt Pachent scored the only goal of the game in his first start for Ringmer as they triumphed 1-0 at Hailsham Town.
Pachent, signed from Whitehawk, rifled the ball home on 14 minutes. Assistant boss Adam Brown, taking charge of the side, said: "My lads were fantastic tonight. They had so much energy. Aaron MacMillan was man-of-the-match but they all worked so hard."
Matt Huckett scored a late winner as East Preston came from behind to beat Whitehawk 2-1. Earlier, Simon Clayton had cancelled out an opener from Phillips. This was EP's first victory since returning to the top flight of county football.
Horsham YMCA began their campaign with a 2-1 win at home to Hassocks thanks to goals from Matt Duffield and Mark Francis. Luke Flomo was on target for the visitors.
Pagham won 1-0 at home to Sidlesham with a tenth minute strike from Richard Brown while Selsey's match with Littlehampton was postponed.
(Read the Sports Argus every Saturday for in-depth Non-League coverage)
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