Burnley looked a shadow of the side that battled for their Premier League survival at Selhurst Park last season as Crystal Palace showed further signs of improvement under Roy Hodgson.
The Eagles, who didn't pick up any points or score any goals in Frank de Boer's seven-game reign, could've had their fill in a commanding first half performance as the visitors struggled to get to grips with their opponents.
The Clarets were perhaps a touch fortunate not to concede a spot kick as early as the 10th minute when Bakary Sakho went to ground under the challenge of James Tarkowski, who appeared to take the man just before making contact with the ball.
But referee Michael Oliver, who maybe had his decision to award Dele Alli a contentious penalty at Turf Moor in the back of his mind, chose to ignore the appeals and give the Burnley centre back the benefit of the doubt.
The home side made the most of their next opportunity, however, as they went ahead in the 20th minute.
The away side uncharacteristically retreated when Sakho collected Christian Benteke's pass on the left hand side and the Mali international drove in to the box and fired past Nick Pope.
Ben Mee's fantastic intervention minutes later prevented Palace from extending their lead when Wilfried Zaha anticipated Charlie Taylor's pass back, lifted the ball over Pope and with James McArthur expecting a tap in the Burnley defender poked clear off the line.
The hosts were working all angles, with Zaha in-particular proving elusive as he popped up left, right and centre, and it was the former Manchester United winger's delivery that was desperately defended by Tarkowski at the near post as Sakho pounced.
Skipper Luka Milivojevic swung in the resulting corner and Benteke, who used all of his strength to beat both Mee and Sam Vokes in the air, powered a header over the top.
Burnley had to wait until the 36th minute to have a true sight of goal when Vokes glanced a header wide of the upright once the ball had been recycled back out to Johann Berg Gudmundsson on the left.
Ashley Barnes went a touch closer when cushioning Tarkowski's headed assist from Gudmundsson's cross, swinging his left boot at the ball from the edge of the box but Hennessey got a fingertip to the attempt to turn it over.
It was Palace who finished the half strongly and could have been out of sight at the interval.
Pope did well to claw the ball from behind him after Benteke had diverted Patrick van Aanholt's drive on target before Sakho's venomous volley, supplied by Timothy Fosu-Mensah, fizzed just wide of the far post.
Burnley improved after the break but Palace were still good value for their lead as they continued to stretch the visitors.
Barnes and Vokes both saw good headed chances go begging early in the second half but Charlie Taylor put his body on the line with a superb block at the other end to prevent Zaha from netting from close range at the other end.
Spurs winger Georges-Kevin Nkoudou was handed his debut just after the hour and the substitute handed the Clarets the lift that they had craved.
With time wasting away, and Benteke and James McArthur threatening for the home side, the Clarets were denied a late equaliser as Barnes beat Hennessey to Steven Defour's ball over the top but the Welshman did extremely well to save to preserve his side's advantage.
Benteke should have eased the tension for the home supporters late on when getting beyond Mee but the Belgian drilled the ball in to the side-netting.