Minamino, on-loan from Liverpool, gave Saints the lead before Mason Mount converted from the spot for the Blues.
Afterwards, Redmond enthused: "We knew this (Chelsea having possession) was going to be the case, they have new management and a new style of play. We have watched a lot of their video clips, studied them to see how we can nullify the threat and earn our way into the game.
"It was great movement from Takumi Minamino for the goal and it just so happens that I could play him in, he has been great since he has come in and shown his quality.
"Danny Ings, you cannot say a bad thing about him since he has come here but things happen and we had to get back into the game by implementing what we can do. It is a point gained with the results we have had.
"A draw today against a very good side will hopefully give us confidence going forward."