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James bravely nodded Leeds back into the contest in stoppage time at the end of a breathless opening period.
Leeds, who have fallen too close to the relegation zone for comfort, got their reward for a tenacious display in the 63rd minute when a corner fell at the feet of Diego Llorente and he fired home from close range.
The draw left Leeds in 15th place with 23 points, six points above third-from-bottom Norwich City, while Villa are in 11th place with 27 points.
A scintillating first half was described by Villa manager Steven Gerrard as "chaos" and he was not wrong, although no one was complaining about the rich entertainment on offer.
"It was frantic, end-to-end and 100 mph. We almost brought into the Leeds style and we needed more calm heads out there so it looked more like our style," Gerrard said.
"A draw was the right result. A fun game for the fans tonight but not one for the coaches!"
Former Manchester United winger James got the ball rolling with a low finish in the ninth minute and he came agonisingly close to making it 2-0 with a thumping effort against the crossbar.
Villa made the most of that slice of good fortune and equalised almost immediately when Matty Cash cut a ball back from the byline and Coutinho took a touch before firing a shot on the turn beyond Illan Meslier.
Barcelona loanee Coutinho, who marked his Villa debut with an equaliser at Manchester United last month, then took over.
An exquisite pass sent in Ramsey to beat Meslier in the 38th minute and he produced a carbon copy five minutes later to split the Leeds defence again, this time Ramsey lashing an unstoppable shot into the top corner.
Leeds looked shell shocked but James somehow got his head to a deflected Rodrigo cross to nod over the line and at least send the visitors back to the changing room with hope.
By comparison the second half was uneventful although still highly-entertaining.
Llorente fired in following a poor clearance by Tyrone Mings from a corner and in a frenetic finale tempers began to fray with Villa's Ezri Konsa sent off after catching Meslier with his forearm as a corner was played in.
While there were several candidates for man-of-the-match, Coutinho's display in the first half had Gerrard purring.
"It was vintage Philippe Coutinho tonight. He's certainly getting back close to where he was when the whole world was speaking about him," Gerrard said.
"He will get better and better. He is a joy to work with."