And just as it seemed the half would end goalless, Long showed his predatory instincts with a 42nd-minute strike.
Baba could not decide whether to head clear or knock the ball back to keeper Thibaut Courtois.
And as he hesitated it fell invitingly for Long, who raced in on goal before deftly chipping into the bottom corner.
Unsurprisingly, Baba did not appear for the second half and was replaced by Kenedy.
Chelsea needed a quick response but they found it tough going as Jordy Clasie and Oriol Romeu took a firm hold in midfield.
Ronald Koeman’s men were not content just to sit on their lead, though, and Gary Cahill was a little lucky not to concede a penalty when he upended Austin as the Saints forward bustled his way into the box.
But Chelsea’s persistence finally paid off after 75 minutes.