The first-half goals ensure the in-form Blues are unbeaten in six and have now won their last three away fixtures.
Scotsman Shinnie, who signed from Inverness in the summer, opened the scoring after three minutes when he swept an Oliver Lee cross high past Lee Camp.
Serbia striker Zigic, a veteran of the club's time in the Barclays Premier League, then doubled the lead on 33 minutes, finishing off a neat move involving Lee and Manchester United loanee Jesse Lingard.
After an indifferent start to the campaign, Clark now wants to keep the momentum going.
"We are well aware of what is going on below us, we are not oblivious to that, but we do want to look at what is going on above us and try and crawl that deficit back," he said.
"I knew all along when we had a few indifferent results at the start, and we had one or two blips along the way with not good enough performances, that the lads had given me everything.
"Confidence is high and they are now believing in each other and what we are telling them to do, as it is working. We have got to keep it going.
"Today we have seen how resilient the players are and everyone worked incredibly hard and defended for their lives at times.
"I am delighted with the finishes by both Andrew and Nikola, we were clinical. When they did breach us, my goalkeeper pulled off some magnificent saves."
Bournemouth were looking to win back-to-back games in the second tier of English football for the first time since 1990.
And the Cherries dominated large parts of the game but could not find a way past an inspired Darren Randolph.
Top-scorer Lewis Grabban had a header superbly saved by the goalkeeper after 21 minutes before Marc Pugh, Matt Ritchie and Ryan Fraser also saw goal-bound efforts kept out.
Bournemouth boss Eddie Howe said: "It is difficult to sum up as I thought we were excellent.
"We were on a high going into the game and but for the early goal I thought we would have won the game comfortably.
"We did everything but score and were the most dominant team. I wouldn't change much about the performance, the level was very high. If we give that performance on average over 10 games we will probably win nine of them.
"We certainly should have scored today and are really disappointed not to do so, but results can cloud everyone's perception of what they have seen."