Poor set-piece defending allowed Gabriel Agbonlahor to open the scoring for the visitors, then Senderos and his team-mates produced an excellent collective display to keep out last season's Premier League runners-up.
Brendan Rodgers' reign as Liverpool manager has been a tale of continued improvement over the past two seasons, but facing Villa on home turf remains something of a sticking point.
Liverpool came back to scramble a 2-2 draw last term and Villa were 3-1 victors on Merseyside two years ago.
Three wins and a draw represents Villa's best start to a Premier League campaign for 16 seasons and Senderos was delighted to help his new team-mates maintain their status as Liverpool's unwelcome guests.
"Not many teams will come here and get a win," he told Sky Sports. "We showed a lot of character and I thought it was a brilliant performance.
"From Gabby upfront, I thought everyone did their job brilliantly.
"We showed some brilliant character. Everyone was fighting until the end. We hung on and it is a brilliant win for us."
Agbonlahor celebrated signing a new four-year contract this week in fine style, showing impressive discipline to restrict Steven Gerrard's influence at the base of Liverpool's midfield after his decisive strike.
"It's down to the tactics we had for the game," the forward told Sky Sports. "We came here with tactics to frustrate Liverpool and try and nick a goal. They came off perfectly for us.
"That was my job, to try and frustrate [Gerrard]. I think everyone knows what Steven Gerrard can do on the ball - you can't give him that sort of space."
On his goal, Agbonlahor added: "It wasn't the best of goals but I think you take them in the Premier League when they come. It tops off a really good week for me."
