Daryl Murphy’s header rescued a point for Ipswich as Bournemouth lost ground on Championship leaders Derby.
Yann Kermorgant’s scissors kick gave Bournemouth the lead but Ipswich pulled level through Teddy Bishop’s side-foot.
Ritchie’s close-range shot at the back post put Bournemouth back in front, but Murphy equalised with a header from Paul Anderson’s free-kick.
The result put Bournemouth three points behind Derby, with Ipswich a point further behind in fourth.
The Cherries began at a blistering pace with Ritchie thumping the bar from 18 yards before Kermorgant found the net with a superb strike for his fourth of the season.
Bournemouth continued to press and Ipswich had goalkeeper Bartosz Bialkowski to thank after he denied Marc Pugh, Callum Wilson and Ritchie in quick succession.
Ipswich grew into the game as the half wore on and a header by Murphy glanced the crossbar.
Cherries keeper Artur Boruc was also called into action before the break, first saving David McGoldrick’s strike with his legs, before tipping Christophe Berra’s header over the bar.
However, Ipswich equalised five minutes after half-time as Bishop converted Tyrone Mings’ cross from 12 yards.
That scoreline lasted just four minutes as Bournemouth went back in front, Wilson finding Ritchie, who converted at the back post.
Bournemouth were denied a penalty after substitute Tokelo Rantie was sandwiched by two Ipswich defenders, an incident that resulted in the South Africa striker being stretchered off and forced 12 minutes of stoppage time.
Pugh’s shot was then well saved by Bialkowski, but it was Ipswich who scored next with Murphy’s header from Anderson’s swung free-kick to make it 2-2.
Bournemouth pushed for a winner, with Pugh curling a shot just wide and seeing another effort saved, while Harry Arter blazed over the bar and Brett Pitman wasted another chance in added time.