Scottish summer signing from Inverness, Shinnie, scored his first league goal for the club after just three minutes, smashing an Oliver Lee cross high past Lee Camp.
Serbian international striker Zigic doubled the lead against the run of play on 34 minutes, latching on to Jesse Lingard's defence-splitting pass to calmly slot under Camp for his fourth league goal of the season.
The Blues are now unbeaten in six but it was another disappointing home result for Eddie Howe's men, who have not picked up three points at the Goldsands Stadium for more than two months.
Bournemouth, fresh from ending Reading's unbeaten home run and picking up their first win in eight last weekend, responded strongly to conceding the early opener and quickly went in search of the equaliser.
The home side were dominating play and Cherries top-scorer Grabban thought he had levelled after 21 minutes but saw Randolph make a stunning flying save to tip his header around the post.
It proved to be a crucial stop as the clinical Blues broke away once more through Lee 10 minutes later, with the ball finding its way to 6ft 7in Zigic who made no mistake.
Bournemouth made a desperate attempt to pull one back before the break.
The in-form Matt Ritchie had a goalbound shot blocked by Paul Robinson on 43 minutes and seconds later Grabban dragged an angled effort wide of the post when through one-on-one with Randolph.
The visiting keeper was called back into action straight after the restart with his goal under siege.
Tricky winger Ritchie could not find a way past after 52 minutes before Pugh's powerful volley was smartly saved by the keeper moments later.
Former Millwall forward Grabban was next to try his luck, heading a curling Ritchie cross inches over Randolph's bar just past the hour.
The away side were soaking up the pressure but still catching their opponents on the break and could have extended their lead further through Manchester United loanee Lingard but for a last-ditch Tommy Elphick tackle.
Elphick and defensive partner Steve Cook were busy in the other penalty area as well, both meeting corners from Ritchie but glancing headers just wide.
Record signing Tokelo Rantie was introduced to try and inspire a Bournemouth goal but it was fellow substitute Ryan Fraser who came closest in the dying moments, having a header spectacularly saved by Randolph.
The game ended with the travelling support in full voice, even giving a brief sample of Christmas songs to mark the occasion.
- Sports & Recreation
- Darren Randolph
- Jesse Lingard
- Lewis Grabban
- Matt Ritchie