Belgium striker Christian Benteke, with his 14th league goal of the season, fired Villa into a first-half lead but the game changed in the first 15 minutes of the second half.
Henderson equalised on 47 minutes and Gerrard scored with a penalty on the hour to leave Villa stuck in the bottom three.
Reading prop up the standings on 23 points from 31 games. Villa have 30 from 31, with Wigan Athletic sitting just above the drop zone.
Just four points separate Southampton, in 12th place, and Villa in 18th and Villa coach Paul Lambert said his side were playing well enough to escape the drop.
Villa are one of just seven clubs to have been ever-present in the top flight since the Premier League era began in 1992.
"We are certainly playing well enough to go and win games," Lambert told Sky Sports.
"Anybody who was here today would say the same - we're certainly playing well enough. We don't look like a team which is down there at the bottom. If we keep going the way we are going we'll win more games than not.
"We have to try and keep confidence - confidence is a big part of the game. That is something that is not lacking with us."
TERRIFIC WIN
Villa, who had enjoyed back-to-back wins over fellow strugglers Reading and QPR, will pin their hopes on the continued goals of Benteke to stay up.
The burly striker put Villa ahead on 31 minutes when a long ball forward was steered down by Gabriel Agbonlahor and the Belgian struck a low first-time shot past Pepe Reina.
Liverpool finished the half strongly with Brad Guzan saving from Luis Suarez and Gerrard and the visitors turned the game around after the break.
Henderson ran on to Philippe Coutinho's pass to beat Guzan and make it 1-1.
Coutinho was then clean through but steered his shot wide and Glen Johnson hit the post but Liverpool got the second goal their pressure deserved when Suarez was carelessly fouled by Nathan Baker and Gerrard scored from the spot.
Liverpool manager Brendan Rodgers hailed a "terrific" win for his seventh-placed side, who are seven points behind Chelsea who occupy the last Champions League place.
"Our character was outstanding today," he said.
"Our quality was there for all to see, and the rhythm and flow of our passing was improved."
