The win moved Barcelona a step closer to lifting the Primera Division title.
Wounded from their Champions League semi-final humiliation at the hands of Bayern Munich, Barca looked in danger of suffering another major setback as Ruben Perez put Betis 2-1 ahead just before the break at the Nou Camp.
If that scoreline had remained the same, then Barca could have seen their once-mighty lead at the top of the Primera Division cut to just five points by nearest challengers Real Madrid when the reigning champions faced Malaga in midweek.
However, three second-half goals, two of them by substitute Lionel Messi, saw Barca recover to claim a 4-2 win over Betis to move 11 points clear of Madrid again and, with only four rounds to go, that means if Jose Mourinho's men do not win on Wednesday, the title will be going to the Nou Camp.
Vilanova said: "Finding ourselves a goal down in the first minute wasn't easy, but the players showed their personality. And more so when the second went in before half-time. It was a question of not losing our heads."
Regarding the possibility of winning the title without even playing in midweek, Vilanova is doubtful.
He said: "Madrid are having a spectacular second half to the season and won't allow slips. We have to think that we still need to pick up two points because Madrid will win them all."
Vilanova also confirmed he would be returning to New York this week for follow-up tests having spent two months in America earlier this year undergoing radiotherapy and chemotherapy treatment for cancer. He is set to be back in Barcelona on Thursday.
Looking further ahead, the Barca coach admits there is plenty to improve on following a testing season on and off the pitch with illnesses, injuries and some surprise results, including their 7-0 aggregate Champions League mauling by Bayern.
He said: "We always must try to improve. This year has taught us all a lot because of everything we experienced.
"It has been a difficult year because of the injuries and because the head coach wasn't here for two months. Next season things will be different, although that's normal because it's my first year."