Against Southampton they had to win because they are one of the weakest teams in the Premier League and Chelsea have a very tough fight with City and Nottingham for the top 4, so it is very important for them to get points and after two defeats against Aston Villa and Brighton they needed this win. Then there is a match against Leicester which they also have to win, and then two tough games against Arsenal and Tottenham.
Chelsea managed to beat Southampton with a fairly convincing score and they did not get a very difficult resistance in the match because Chelsea could play much more dominantly than Southampton who only defended. This victory does not completely secure Chelsea in the top four of the standings because Man City have not played their match, so if Man City wins the match, Chelsea will drop back down in their current standings.
Chelsea will face a tough match in the future because it will face Arsenal and Tottenham but before they have to face several other matches. If it is unable to maintain the best momentum, it is feared that the top five positions will be taken over by the challengers below.