Baber's men held their nerve despite knowing defeat would have seriously dented their chances of reaching the knockout stages after Edinburgh's win over Racing Metro and the former scrum-half praised the manner in which they kept their focus throughout an 80-minute arm wrestle.
"The Edinburgh result focused the mind somewhat but the whole focus this week was on controlling what we were doing regardless of what happened last night in Paris. We're pleased that we kept that focus in the build up and we certainly kept our focus in the game," said Baber, whose men have picked up three of their four victories by seven points or less.
"Getting over the finishing line was everything. We came away with a victory so I'm very pleased.
"When we played them at home, even though they were down to 14 men, they pressurised us and created a game that tested us defensively. And there were stages in today's game where they did exactly the same.
"But we controlled the field when we needed to and then we had a bit of brilliance from Casey Laulala which was finished off by Sam Warburton. You saw a good team performance in managing the game and getting the victory. That was also down to Leigh Halfpenny and his kicking.
"I thought we were good in certain aspects - we pushed the ball through the hands and tested them defensively, then we came out after half-time and we seized the initiative and that's something we've talked about as a group. We've talked about being accurate and sharp and creating momentum at the start of the second half and I thought we did that very well. Plus we pressurised them into giving us penalties that allowed us to keep the scoreboard ticking over.
"They looked at ways of undoing us with ball in hand and we obviously looked to counter act that and I thought we were good for the win. The game got a little bit narrow and we started to dominate in terms of our defensive shape.
"We infringed a little bit too much, though, and that kept them in the game. I also think that if we had been a little bit more accurate in holding on to the ball we probably could have squeezed a little bit more out of the match."
The victory means the Blues know that if they match Edinburgh's result against Irish when they take on Racing next Sunday they will finish as pool winners.
Baber is aware that improvements can, and must, still be made, though, and he insists the Blues won't be resting on their laurels or taking anything for granted on home soil.
"The goal is very straightforward in terms of the maths but Racing will be looking to make amends for us winning out there at the beginning of the group phase. They'll also be hurting from their loss to Edinburgh so they'll have something to say about it," added Baber.
"It's important that we stick to our planning and get our week's work right going into that game.
"We'll take what we've achieved today because it's been hard work from the players - and not just this game, but all week and all season - and then we'll get together on Monday and see what we've got ahead of us with Racing.
"The players are the most critical of themselves and they'll have a look on Monday and see how they can sharpen things up."