Leeds went ahead in the ninth minute through a terrific strike from James who was then denied a brilliant second in the 29th minute as his shot from the edge of the box smashed back off the crossbar.
But Villa levelled less than 60 seconds later after a fine finish from Philippe Coutinho who then produced more magic to set up Jacob Ramsey to fire Villa in front seven minutes before the break.
The same pair then combined five minutes later as Villa bagged their third, Ramsey smashing home a clinical finish into the top right corner after the Brazilian's through ball.
But Leeds pulled a goal back in the second minute of first-half stoppage time as James scrambled home a header from close range to double his tally and the Whites equalised in the 63rd minute as Diego Llorente converted from a corner.
Villa's Ezri Konsa was then sent off following a second booking after catching Meslier with his elbow with three minutes left and after eight minutes of added time a thrilling contest ended all square.
Graham Smyth, the YEP's chief football writer, hands out the scores.
1. Illan Meslier
7 - Left unprotected for both of Ramsey's goals. Didn't have much to do apart from pick the ball out and gather a few crosses. Photo by Alex Livesey/Getty Images.
2. Luke Ayling
6 - Found it hard to lock down his side of the pitch defensively, lost Coutinho for one of the goals. Kept trying to get Leeds going forward. Photo by Clive Mason/Getty Images.
3. Diego Llorente
7 - He was left chasing shadows at times thanks to Coutinho's passing as Villa got in behind. Battled, passed it well, took his goal well. Photo by OLI SCARFF/AFP via Getty Images.
4. Pascal Struijk
7 - Some lovely passing, lots of fight and provided an attacking threat from corners. Photo by George Wood/Getty Images.
5. Stuart Dallas
6 - Kept going, linked up well down the left. Like Ayling, he couldn't stop Villa from exploiting space in behind him. Photo by Catherine Ivill/Getty Images.
6. Robin Koch
6 - Couldn't give Leeds control in the middle or stop Villa pouring forward but put in a big shift, got stuck in and tried to move the ball quickly. Photo by OLI SCARFF/AFP via Getty Images.