Chelsea ventured to the north-west to take on a Burnley side that were on a good run of form and returned south with the three points on offer, courtesy of a 2-1 win.
The victory closes the gap between Chelsea, in fifth, and Tottenham Hotspur, in fourth, to five points with just four games to go.
Chelsea still harbour ambitions of a place in the Champions League next season but a more likely scenario is qualification for the Europa League.
Against Burnley, Chelsea took the lead through an on goal by Long who inadvertently turned a cross into his own net.
Burnley equalised in the 64th minute when Ashley Barnes was on hand to score.
But, just five minutes later Chelsea were back in the lead when Victor Moses struck what turned out to be the winning goal.
Next up for Chelsea is an FA Cup semi-final, At Wembley, against Southampton this Sunday.