It was tough luck on Everton who had battled back to level the scores with two second-half goals from Tomasz Radzinski and Kevin Campbell.
But the honours deservedly went to Villa who secured their third home win of the season.
Hendrie, who did little to enhance his prospects when he requested a rest one week after Taylor took over as manager, produced a sparkling performance with his two goals.
However, Villa then allowed Everton back into the game and in a nerve-jangling finish the home fans were only relieved by Dublin's late strike.
Hendrie was one of four changes made by Taylor after last Monday's 3-0 humbling at Birmingham City.
The only surprise was the axing of the transfer-seeking Alpay who, in the opinion of Taylor, had been responsible for two of the three goals conceded at St Andrews.
Villa were fired up from the start with Hendrie, in particular, buzzing against a far from secure Everton defence.
This was emphasised when Hendrie took a pass from Ulises de la Cruz, played a return ball with Darius Vassell, and scooped his shot into the top corner of the net.
Everton, with only one away win to their credit, were far from impressive in the first half. Their lack-lustre attack posed few problems and Peter Enckelman had a trouble-free first half following the bizarre own goal he conceded against Birmingham.
The hugely talented Wayne Rooney was an industrious worker for Everton but he picked up the first booking of the game when he unceremoniously bundled Vassell over the touchline.
However, three minutes later Everton hit back when Thomas Gravesen cut in from the left and the ball bounced into the path of Radzinski who scored with a shot that crept just inside the post.
This was a purple patch for Everton and Enckelman had to make a brilliant save to keep out an effort from Campbell. However, the Everton striker notched his fourth goal of the season in the 67th minute from the resulting corner when he got in front of Peter Crouch to head home.
Vassell went close to scoring Villa's third when Alan Stubbs missed a long clearance from Enckelman but the England striker headed wide.
Vassell made way for Dublin and, in the 85th minute, the former England striker scored Villa's winner.
Mark Kinsella's corner was nudged back into the path of Dublin by Olof Mellberg and the veteran striker scored with a deflected close-range shot