Visiting Everton's best chance of the opening 45 minutes fell to Louis Saha, but the Frenchman shot straight at the returning Shay Given in the Villa goal.
The home side failed to create many goalscoring chances before the break, with their only opportunity falling to Darren Bent who headed over the bar.
The deadlock was eventually broken 11 minutes after the restart courtesy of Bent's seventh goal of the season. Stephen Ireland's flick on found the striker, who chested the ball down before sending a bouncing effort past Tim Howard.
Villa boss Alex McLeish introduced the recently-signed Robbie Keane into the action with nine minutes remaining and the Irishman almost made an instant impact. He found striker partner Bent but Shane Duffy got back to prevent the centre-forward scoring his second of the afternoon.
Anichebe also went close to claiming a brace with time running out, but his shot was held by Given.