It came courtesy of a first-half goal by Kevin Ellison but the margin should have been much greater.
Bournemouth, without a win since early September, provided precious little clout upfront and home keeper Gavin Ward had only one real save to make.
Tranmere were unlucky in the 21st minute when a header by Gareth Taylor was turned on to the bar by Bournemouth keeper Gareth Stewart.
But Tranmere got the all-important goal in the 41st minute. Ellison headed in from close range after Taylor headed back a deep corner by Shane Sherriff.
Ellison was unlucky to head on to the bar two minutes later and then just before the break Sherriff saw a header headed off the line by Stephen Purches.
The Cherries' only first-half effort came from Steven Foley with his shot turned aside for a corner by Ward.
Bournemouth sent on Leon Best in attack after half-time but could not force a breakthrough.
Darren Anderton, who showed his class in midfield, was off-target with two good strikes and Steve Fletcher saw two weak headers easily held by Ward.
Tranmere almost doubled their lead on 73 minutes but a spectacular overhead effort by Chris Greenacre saw Stewart tip the ball over.
Taylor wasted a good chance and then an Ian Goodison header was blocked on the line.
Ellison was excellent for the Merseysiders before being brought off in the 72nd minute.
John Thompson, in his first game on loan, did well in defence and Chris Shuker was always lively in attack.
Best could not really make an impact for Bournemouth after replacing Foley.
Stephen Cooke was also put on in the 63rd minute for Franck Songo'o who did well enough but often retained the ball too long.
Bournemouth are still without an away win and they are worrying times for recently appointed manager, Kevin Bond.
There were bookings for Tranmere's John Mullin, Chris McCready, Shuker and substitute Steve Davies within seconds of going on as a late substitute.
Bournemouth's Shaun Maher and Warren Cummings also went in the book in a somewhat disappointing clash.