The Cherries went in front after just three minutes when Brett Pitman's inswinging free-kick avoided everyone, including goalkeeper James Spencer, and ended up in the back of the net.
Anton Robinson then secured victory when he poked home from close range 11 minutes from time after Spencer had saved Liam Feeney's initial effort.
Tindall said: "There was huge pressure on the players and we've come through that and made sure of three points, so hopefully everybody's happy with that.
"If you'd said to us 15 games ago that we'd have to go to Chester to get a win and give ourselves a good chance of being safe, we'd have bitten your hand off.
"We defended excellently and created a number of chances even if we looked a little nervous at times. The second goal was crucial and as soon as that went in it relieved a lot of the pressure."