Mendes got Reading off to a perfect start with a sixth minute strike but Villa, winners of seven of their previous nine games, restored parity when captain James Chester headed home eight minutes later.
Mendes, though, added his second straight after the break, sweeping home a cross, before Lewis Grabban, provider of the second, converted a penalty in the 79th minute.
With four games to go in England's second-tier league, Reading now have 76 points, one less than Huddersfield Town, who have also played one game fewer.
Reading, though, are three points ahead of Leeds United and four clear of Sheffield Wednesday, the Yorkshire clubs who fill the other two playoff berths.
(Reporting By Tom Hayward; Editing by Ian Chadband)
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