Rafael Benitez's side - unbeaten at home in 2008/09 - started aggressively and should have edged ahead with Fernando Torres, Steven Gerrard and Yossi Benayoun all failing to net following a goal-mouth scramble.
Villa, who had threatened little beforehand, took a surprise lead after 34 minutes, with Lucas Leiva heading an Ashley Young free-kick into his own net.
And the goal proved to spur the visitors on, who bagged a crucial second in the second minute of first-half injury-time as Curtis Davies headed home a corner at the near-post.
The hosts rallied after the break and, after peppering an inspired former Liverpool goalkeeper Brad Friedel in the visitors' goal, deservedly reduced arrears after 72 minutes with Torres volleying home Emiliano Insua's centre.
However, their goose was cooked just three minutes later, as captain Steven Gerrard upended Nigel Reo-Coker inside the danger-zone, allowing Young to coolly convert from 12 yards.
The defeat leaves Liverpool six points adrift of early leaders Tottenham Hotspur and Chelsea, who have both won all three of their opening encounters.
"The first 20 minutes we were alright but an own goal and another goal in (first half) extra time and then a penalty when I thought we were playing better and pushing hard, there were too many things against us," Liverpool manager Rafa Benitez told BBC radio.
Villa, who for much of last season looked capable of a top-four finish before running out of steam, were booed off after losing to Wigan Athletic at home last week but manager Martin O'Neill was delighted with their response.
"We put a big effort into the match, we defended very strongly and we broke. We are capable of scoring goals and we did that," he said.
"I was staggered about what was going on (being booed). For us to get the abuse we got at half-time against Wigan, I don't think it was warranted."
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