After Ashley Barnes had cancelled out a Kevin Long own goal shortly after the hour, Moses’ low strike restored Chelsea’s lead at Turf Moor as they secured a win which maintains their hopes of Champions League qualification.
Antonio Conte’s men are now just five points behind Tottenham in fourth with that gap having been 10 points just last week, before Spurs lost to Manchester City and drew to Brighton.
Chelsea have an FA Cup semi-final to think about next, taking on relegation-threatened Southampton in the final four of the cup at Wembley Stadium on Sunday (3pm).
But their win over the Clarets served as fine preparation with Chelsea overcoming a stern test against Sean Dyche’s high-flying charges.
And captain of the London outfit, Cahill, felt that wide-man Moses was crucial towards earning the full three points.
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I thought he was brilliant, he kept the width really well for us and we managed to get down the side quite often. Down both sides, to be honest with you.
“I thought he was brilliant, he kept the width really well for us and we managed to get down the side quite often. Down both sides, to be honest with you,” he said.
“I just saw him out of the corner of my eye and put him in and a great finish. He was superb. There were a number of players out there who did very well.
“We showed the right character and the right attitude, which is the main thing otherwise you get unstuck at places like this.
“A win away here is very good for us. These [Burnley] have been a credit to themselves this season, they’ve been fantastic.
“[It’s a] Very tough place. They made it tough for us today, throughout the whole game.
“We’re just happy to get the three points. Decent performance from us I thought.”
Cahill was an unused substitute for clashes with Manchester United, City and Spurs but the 32-year-old hopes that his fine display away at Burnley can put him in the frame to feature against the Saints this weekend.
He told Sky Sports: “I’m not putting too much pressure on myself. I know what I’m capable of, I’ve done it for many years.
“It’s just nice to be back out there and playing and getting the results. I think it’s important that you get match fit and match sharp and you don’t get that sat on the bench.
“Regular game time is what you need to get sharp. I’ve been back in the last couple of games and most importantly, we got a good result tonight.
“We take some momentum now into what is a very important weekend for us.”