Beckford came off the bench at Goodison Park last night to open his Premier League goalscoring account by curling home a brilliant leveller for the 10-man Toffees deep into injury time.
The 26-year-old has struggled to make an impact since his free transfer from Leeds in the summer - netting just once previously with a penalty in a Carling Cup tie against Huddersfield - but Baines hopes the corner may now have been turned.
Baines, who robbed Lee Chung-yong to set up Beckford's strike, said: "It is a great goal to get Becks off the mark in the Premier League.
"He'll feel good for it but he has been doing it quite regularly in training. He has looked sharp.
"Early on in the season he was thrust in a bit because we were short on numbers but now the manager will be able to do it the way he would like to and introduce him gradually.
"He has now proved he can be a valuable asset for the club, coming on and scoring goals like that."
Beckford's goal cancelled out a 79th-minute effort from another substitute, Ivan Klasnic, and snatched a 1-1 draw to extend Everton's unbeaten run to seven games.
The Merseysiders' night had seemed destined to end in misery when Marouane Fellaini was sent off for kicking Paul Robinson between the legs four minutes from time.
Matt Taylor also hit the bar for Bolton but Everton enjoyed several spells of pressure and Baines felt the hosts got the least they deserved.
The 25-year-old left-back said: "I think we were worthy of a point. We struggled at times to break Bolton down - teams tend to come here and pay us a bit of respect and sit back.
"It makes it difficult for us and Bolton did that quite well.
"We struggled to create any really clear-cut opportunities but we did have a few chances to score goals.
"We passed it quite a bit but never had that bit of quality to find a goal.
"In the end we ended up nicking a point in the last minute with a great goal.
"There is a consolation in that we remain unbeaten and hopefully we can continue that."
Bolton would have gone fifth in the table had they managed to hold on for victory.
But they still remain in a highly creditable sixth place heading into this weekend's clash at Wolves and the players have been quick to rally around Lee following the error that allowed Baines to pounce.
Captain Kevin Davies said: "We should have seen the game out but these things happen in football.
"The lads are a bit down but we will pick ourselves up.
"It is a difficult place to come but we have not got anything here for a few years so we have to take the positives.
"The lads have been brilliant with Lee.
"As the manager says, he has been outstanding for us. He is a young player and he will learn from it.
"He is a little bit down but we will pick him up - we win together and we lose together."
Bolton can still reflect on a satisfactory few days having beaten Tottenham 4-2 in thrilling fashion last week.
Veteran forward Davies, 33, added: "It's four points we'd probably have taken.
"This is two points gone away but we will take it down to Wolves, which will be another tough game.
"Our performance wasn't as good as it was at the weekend but it is still a good result.
"The lads are lively and chirpy and we will move on. We'll use this towards getting a bit of a run going."