He was on target five minutes from time as Posh made it two straight wins in a result that left Boston still searching for their first point.
Both sides had played a part in the lively opening exchanges, but few clear chances arrived.
The best early moments for Boston were two off target long-range drives by Jamie Clarke and David Galbraith, while Posh responded with a forceful header by Guy Branston from a Jamie Day corner but the ball flew too high.
The visitors picked up the tempo and almost went ahead on 21 minutes.
Danny Crow evaded keeper Andy Marriott on the edge of the box and squared to Lloyd Opara but his shot was blocked by Mark Albrighton.
Moments later Day fired a low ball into the home danger area where Albrighton was relieved to slice the ball past his own post.
Boston hit back from a 34th minute Galbraith corner when first Mark Greaves looped a header against a bar and then Albrighton forced a tip over save from Mark Tyler.
Back at the other end Marriott made a good save to thwart a low drive by Opara.
And Marriott was again in action seconds after the restart tipping over a fierce 20-yard snap-shot by Yeo.
Peterborough though had their task made tougher on 50 minutes when Opara was shown a straight red card by referee Andy D'Urso for appearing to elbow Albrighton in an aerial challenge.
Boston then stepped up the pressure and, for a spell, pressed Posh into their own third of the pitch.
Clarke and Francis Green forced good saves from Tyler as the tempo increased.
Peterborough counter attacked on 75 minutes as Richard Butcher broke down the right but he was unable to prevent Marriott from clutching his low cross.
But Posh defied the numerical deficiency to take an 86th minute lead when Yeo scrambled in a close-range header after the ball looped up off Paul Ellender following Jude Stirling's driven cross.