Chelsea found themselves behind almost immediately after Essien sent the ball over Cahill for Rodriguez to calmly slot home.
Southampton keeper Artur Boruc then saved Oscar's shot before James Ward-Prowse curled a free kick wide for the Saints as Essien was clearly outpaced and Southampton dominated in midfield.
Things changed after halftime as Chelsea gradually took the upper hand and was rewarded when Juan Mata's set-piece found Branislav Ivanovic, whose header was redirected by Ba onto the post before Cahill headed the ball in from the rebound.
Terry then rose above defenders following a half-cleared corner to send Stamford Bridge into rapture and Ba finally added the third after converting a Ramires cross.
"After we got the first goal it was fairly even sided," said Southampton manager Mauricio Pochettino. "We are unhappy but there were a number of decisions that did not go our way. The ones you don't see are perhaps more important. There was no doubt that the players will react positively. But lest we forget we were playing Chelsea."