After securing their first win of the campaign with a 3-0 home victory over West Ham before September's worldwide break, the 31-year-old now believes that Newcastle can get their season off properly - starting with another possible three points against the Swans.
Jamaal Lascelles scored the only goal of the game with a thumping header in the 76th minute.
Just past the hour mark defender Lascelles made a last-ditch intervention as Swansea's Tammy Abraham rounded Newcastle keeper Rob Elliot and shot goalwards only to see Lascelles move in and prevent a certain goal.
The 57-year-old Benitez wasn't at Liberty Stadium after having a procedure tomorrow to address an infection resulting from an earlier hernia operation.
Newcastle assistant manager Francisco de Miguel Moreno said: "Rafa wanted to come and wanted to do everything he could to attend, but the weather conditions were not the best".
"We were very serious in some stages of the game, we were very compact, disciplined and worked hard together".
"After the game Rafa rang and he has congratulated everybody, especially the players because they have done a massive job". They had only three points on the board after seven games and had only won five games in the calendar year of 2014 while Swansea, by contrast, were enjoying an excellent start to the season under Garry Monk and were fourth in the table.
Newcastle went closer after 33 minutes when Ritchie's cross was met by the head of Joselu and Fabianski sprang to his left to pull off a fantastic one-handed save.
As for Swansea boss Paul Clement, he has lost his top two goalscorers from last season in Gylfi Sigurdsson and Fernando Llorente but he brought in Wilfried Bony and Renato Sanches on transfer deadline day to surprise everyone.
Paul Clement introduced returning striker Wilfried Bony in his place but the fan favourite could do little about Lascelles' thumping victor, the captain getting above Alfie Mawson to leave Fabianski with no chance.
"We have set a standard now". It wasn't good. But I thought we gave a proper performance against West Ham.