The two sides meet at Stamford Bridge on Saturday and the Portuguese boss has warned his players about complacency ahead of the fixture
Everton currently sits 13th in the table having lost its last two matches against Manchester City and, more recently, Liverpool but Villas-Boas maintains his side must be wary of the performances from Moyes' charges.
"Everton were on a very good run in my opinion," Villas-Boas told reporters. "They lost against Liverpool but had they won they would be up challenging for the top with one game in hand. So they are in a good situation and once again proving that David Moyes' work is something fantastic."
Everton has gained a point from each of its last three league trips to Stamford Bridge but Villas-Boas maintains his side can secure victory to keep up with the Premier League pacesetters.
"It's motivation and the players' belief that they can do it," he said. "They believe they can come out of Stamford Bridge with points because it has been happening in the past. In football and paper things look different but surprises happen, it's why I don't believe in having a favorites role in every game we play because the unpredictable can happen.
"To emphasis the importance of our game, Everton is looking for the sixth game unbeaten coming to the Bridge. We have to be alert and it is going to be a hard battle."