Scotland fly-half Parks kicked 20 points in last weekend's 25-8 win over the Scottish side in the Welsh capital, a victory which sent the Blues top of Pool Two.
Despite that the former Glasgow man still came in for criticism from fans and pundits alike after a display dominated by his kicking from hand.
But Baber says the 33-year-old is doing a great job for his side, even if he may not be a crowd-pleaser.
Baber said: "If you see the games we have won this year, one of the main reasons has been the control Dan puts on the game.
"I understand the public and the press want to see an open game but at times in Europe you have to control the game away from the opposition, like Ronan O'Gara does for Munster.
"That is what Dan does for us and he was very good last week and in the previous games in the Heineken Cup. Against Racing Metro we scored two tries through using width and he was a big part of that, which shows he can mix it up.
"People don't realise that an effective kicking game from your number 10, as long as you create options around him to play, is difficult to defend.
"We have options like Jamie Roberts, Casey Laulala and Alex Cuthbert to bring into the game. Dan is just doing what I ask him to do."
Victory at Murrayfield on Friday night would put the Blues within touching distance of a first quarter-final appearance in three years, but Baber insists his side's position is far from comfortable and there is still much work to be done.
He said: "We are not comfortable, that is not how we see it.
"If we go there and lose it's not the end of the world but people start to look over their shoulders and that's where the pressure comes from. We have been afforded an opportunity to nail the group, but it's not a comfortable position to be in and the players said after the win on Friday that we still have three games to go.
"It's crucial to get a performance on Friday and in the next two games as we need to keep driving on and get that momentum which is so powerful when you have it.
"Edinburgh will be hurting after last Friday and will want to come out and test us and create opportunities for themselves. They are going to fancy themselves at home and we will have to work hard to negate that and impose our game plan."
Baber had hoped to give Gavin Henson a debut for the Blues, but the Wales centre is not named in their matchday 23, with injury to wing Cuthbert seeing Gavin Evans come into the side as the only change from last weekend's victory.