Moussa Djenepo scored his first home goal for Southampton in the 41st minute and Oriol Romeu smacked home a sensational volley with just over 20 minutes remaining as the Saints kept their second clean sheet in two games.
Next up for Halep is another 19-year-old youngster, Iga Swiatek of Poland, whom Halep defeated in the round of 16 here last year.
Matthaeus encouraged Schalke not to give up as 31 rounds of matches still remain.
"We grew up playing together. (Rublev) has improved a lot ... It is very important for me to take this opportunity and fight harder this time, maybe do something better, " said Tsitsipas, who has lost all the two previous encounters on the Tour with Rublev as the recent one was just eight days ago at Hamburg Open final.
The visitors from Poprad did not put on an offensive show either, but scored twice, which was sufficient for earning their first victory of the season.
Sevilla presented their last two signings of the summer with Karim Rekik and Oussama Idrissi joining Julen Lopetegui's side, who once again look to have worked well in the transfer market, despite failing to sign Real Sociedad's Willian Jose.
The player was found guilty of demonstrating "a discriminatory gesture," during the AFC Champions League game against Pakhtakor on September 30, 2020, in Doha.
The attacking-minded player, who began his career with Osasuna, joins Athletic Bilbao after 72 appearances in Serie A in which he scored eight goals and provided seven assists.
"I hope the crisis makes the clubs to rethink their strategy and increase their efforts to give space for young talents," he added.
Early indications are that Carvajal could be out of action for up to two months, which means as well as the forthcoming internationals, he will also have to sit out this weekend's La Liga trip to play Levante, and league matches against Cadiz, Huesca, Valencia and Villarreal.
Kitata, 24, managed to dash to the finishing line first, one second before Kenya's Vincent Kipchumba.