After Friday's convincing 7-0 win at Bishop's Stortford, Glenn Roeder's men were handed a much tougher task against second division Posh, who fought their Premiership opponents for the entire 90 minutes and came close to scoring on several occasions.
However, the outing was still a comfortable one for the Hammers, who fielded an almost unchanged line-up from that which triumphed at Stortford, with the exception being the inclusion of French trialist Lauren Courtois, who replaced the injured Joe Cole on the left side.
The visitors took the lead after just 10 minutes, when Paolo Di Canio's quickly taken free-kick on the right released Trevor Sinclair, who squared the ball for Kanoute to fire past Tyler in the Peterborough goal.
Goalmouth action was at a premium for the rest of the half, although Fredi should have doubled his tally on the stroke of the interval when Carrick sent him clean through on goal.
However, rather than shoot as he entered the penalty area, the Frenchman attempted to round the goalkeeper and saw the ball touched from his toe to Courtois, whose follow-up effort was blocked.
The second half failed to provide many more glimpses of excitement, although Peterborough looked more likely to grab an equaliser as the game wore on. Sebastien Schemmel was on hand to block one goalbound header on the line, but other than that the hosts failed to seriously trouble David James, who impressed with a commanding display of athleticism and confidence.
The England keeper was fautless in his kicking and handled crosses superbly, although he did accidentally injure Australian defender Hayden Foxe when he raced to the edge of his box to punch away a long ball at the start of the second half.
Victory was sealed three minutes from the end, when Jermain Defoe, on as a substitute for Kanoute just 10 minutes earlier, proved what a valuable option he could prove to be for Glenn Roeder this season when he picked up the ball some 30 yards out and advanced to the edge of the area before firing a low shot past Tyler.
While Courtois quietly impressed in a wide left role in midfield, fellow French trialist Ludovic Asuar was on show for the final 19 minutes and did enough to suggest that he will be worth another look in the Hammers' next pre-season work-out, at Stevenage Borough next Monday (July 30).
West Ham: James, Schemmel, Winterburn (Byrne 68), Moncur (Asuar 71), Dailly, Foxe (Soma 49), Sinclair (Potts 82), Carrick, Kanoute (Defoe 77), Di Canio (Kitson 77), Courtois (McCann 84).