The Toffees looked to be cruising against West Brom after the left-back's two goals had put them in a comfortable position at half-time only for substitute Shane Long to set up a nervy finish.
Aston Villa are next up at Goodison Park on Saturday and with fellow strugglers Norwich and Reading to come in February - plus a trip to Old Trafford - before a tricky-looking run-in Baines thinks they have to capitalise now.
"The big games away from home are still to come so these are the games which are really important to win," said the England international.
"We don't want to be dropping points in these games because it puts extra importance on the tougher games.
"It was a massive three points (against West Brom) as we start to draw in on the tail-end of the season.
"It is important to keep winning and keep ourselves in a strong position and it takes us forward into another big game at the weekend.
"It would be nice to win every game three or four nil but that's not the case and we showed character to hang on in there and win the game.
"That is important at any stage of the season because you don't want to be dropping points from winning positions.
"I think we've got better at it but it is never easy when you are ahead and you give up a goal and the opposition get their tails up and you have to weather the storm.
"It is something we have been learning over the last few years as we have improved and I think we are getting better."
Something else they are also improving at is spreading goals throughout the team with Baines' double taking his tally to six for the campaign, just one behind striker Nikica Jelavic and two adrift of Marouane Fellaini.
A total of 13 players have found the net this season and Baines believes they have to keep sharing the load if they are to stay in the hunt for Champions League football, being a point off fourth and only five behind third-placed Chelsea.
"When we play at home the onus is on us. We have to find ways of getting the goals and winning the games," he added.
"Different weeks there will be different people who come to the fore and that has been the way all season.
"The important thing is someone keeps popping up and doing it."
West Brom boss Steve Clarke hopes the return from injury of the likes of Long and Claudio Yacob will help lift them out of their current slump of one point from a possible 15.
"Shane scored almost immediately after he came on - that is what he does- and it is good for us we got him back on the pitch because he's been out for a number of weeks and he hasn't trained very much with the team," said the Scot.
"I would have loved to have started with him but sometimes you have to protect the player for the long-term and because you get them out the treatment room it doesn't mean they are ready and firing to go into matches.
"I think in the next couple of games we will get the team back up to speed and see a return to the results and performances of earlier in the season."