Philip Billing slammed home his sixth goal of the season to give the Cherries a first-half lead, which was doubled by Arnaut Danjuma's well-placed finish in the 75th minute – his fourth in five games.
Asmir Begovic saved Adam Armstrong's injury-time penalty as Bournemouth kept a second clean sheet in three games to stay a point behind sixth-placed Reading after registering their first ever league double over Blackburn.
And a delighted Woodgate said: "We ground it out. It was a professional performance.
"We can play better at times but it's a sign of a good team when you can grind out results and I thought we did that.
"I think since I've been here we've only had one defeat away from home so we've improved that side of the game, which we needed to do.
"Coming away from home, it's not all about being pretty. It's about getting results and we did that today. Today we were more clinical in both boxes.
"Ugly Bournemouth, I'll take it all day long. Sometimes people say pretty Bournemouth, soft and all that. Not at the minute.
"It was a strong performance. It's not all going to be perfect and sunny every single day. Sometimes you've got to really grind results out and we did that.
"We weren't at our most fluent today but that happens. A very good four days over Easter."
Blackburn's wretched run of form continued – they have now taken only seven points from the last 42 available, with one win in those 14 games, and manager Tony Mowbray admitted scoring goals is "an issue".
He said: "We gave a good account of ourselves in the first half without reaching the levels we know we can reach. We threatened their goal more than they threatened ours in the first half, yet you could always feel their individual quality.
"Their goal first half came out of nothing. At this moment, those sort of moments aren't going our way.
"This team can win football matches. We've been without our two main goalscorers for recent weeks. It's hard to win football matches when you don't score goals. Without (Bradley) Dack and Armstrong, it's an issue for the team to score.
"We missed another penalty, we had one or two half-chances, they kicked one off the line late on. Probably not enough. I'm not sure they played well enough to think they deserved to win 2-0.
"These players are good players but you need the guy to stick the ball in the back of the net out of nothing, like their first goal today."