A freak second-half goal from Ryan Fraser spared the Cherries' blushes, cancelling out Kieffer Moore's opener.
Hot on the heels of their rivals, the in-form visitors made the 48-mile trip to Huish Park two points outside the Sky Bet Championship top six and came up against a side they had beaten eight times in their last 10 meetings.
Cherries winger Matt Ritchie scored twice inside the opening 20 minutes to inspire his side to victory against Reading on Tuesday, and the 24-year-old should have notched another early opener on two minutes but blazed Lewis Grabban's cross over the bar.
However, it was Yeovil - who came into the match six points from safety - that shaded an open first half and nearly snatched an early lead when Joe Edwards evaded Ian Harte and pulled the back to James Hayter, but the ex-Bournemouth striker fluffed his lines.
The visitors had found the net 14 times in their previous five matches before arriving in Somerset, and their attacking prowess was evident when Fraser, who replaced Marc Pugh in Eddie Howe's only change from Tuesday's win, called Marek Stech into action with a low shot.
With the Yeovil fans and players growing increasingly irate at referee Robert Madley, their anger turned to joy on 25 minutes when former Dorchester striker Moore threatened to derail Bournemouth's late promotion charge.
A seemingly routine free-kick into the Cherries box by Jamie McAllister was headed clear but fell to Moore at the edge of the box, and the youngster rifled an unstoppable volley into the top corner.
Bournemouth responded well and ended the first half strongly with the lively Grabban spurning two good chances before the break, twice firing wide after good work from Ritchie and strike partner Yann Kermorgant.
Shortly after half-time, the visitors thought they should have had a penalty after Byron Webster appeared to handle in the area, but moments later drew level through a freak goal.
With the Cherries turning the screw, Webster attempted to clear from inside his own box but the ball cannoned into Fraser and looped over Stech and into the net.
With four games now left to decide their fate, Yeovil responded well to the setback as Moore dragged a shot narrowly wide before Bournemouth winger Ritchie threatened to complete a quickfire comeback for the visitors.
Eyeing a sixth successive league win, the Cherries poured forward in search for a late winner but almost left themselves open at the back when Manchester United loanee Tom Lawrence weaved his way into the box, but his curling shot crept wide as the match gradually petered out.