Recently returned from a spell in New Zealand, Yeo steered in a far-post header with five minutes left after Lincoln looked set to go down to a spectacular goal on the half hour mark from their former player Peter Gain.
One-time Spurs junior Gain spent five years at Sincil Bank before being tempted south by Posh boss Mark Wright last summer and had been on the receiving end from over 1,600 travelling Lincoln fans through the opening 30 minutes.
Gain answered them in superb style. Taking a lay-off from James Quinn after Lincoln only partially cleared a Jamie Day corner, he let fly with a left-foot shot that soared past helpless goalkeeper Alan Marriott and into the top corner of the net.
Both sides put the emphasis on attack to produce a highly entertaining clash that displayed passion and skill in equal proportions.
Only a minute before Gain's goal, Marriott flung himself to make a finger-tip save and deny Northern Ireland international Quinn, who put in a well-placed header from Adam Newton's neat cross.
Lincoln also had their chances early on with Yeo and defender Jamie McCombe both sending shots narrowly wide.
With manager Keith Alexander using all three subs Lincoln came back strongly after the break and former Posh man Francis Green, newly back from a loan spell at Boston, tested Mark Tyler.
Posh defenders Mark Arber and midweek signing Phil Bolland produced some timely tackles as Lincoln took the momentum and when Nat Brown did get through, Tyler saved impressively and then confidently with the resulting corner.
But Posh again failed to hang on to a lead and Yeo's 85th minute effort extended Lincoln's unbeaten run to four games.