Peterborough 0, West Brom 2: FA Cup joy for the Baggies
But the second goal, which Albion had threatened since Simpson's opener, arrived in the 37th minute.
A superb curling cross from the right flank by Kim Do-Heon was met by an unmarked Robinson at the far post. The Albion defender sent a powerful downward header into the far corner with Lewis unable to get a hand to it.
But the visitors were fortunate moments later when a corner from Dean Keates caused confusion in the Peterborough defence and Carson misjudged his attempted punch.
The ball fell to Aaron McLean but referee Andy D'Urso adjudged that the Peterborough striker had fouled a defender in his bid to head the loose ball home.
Bednar then squandered a great chance to make it 3-0 in the 41st minute when he sent his shot over the crossbar from just 12 yards.
Albion continued to dominate after the interval and in the 52nd minute a cross from Greening was met by Bednar at the near post.
However, the Albion striker's diving header lacked direction and it flew wide of the target to the relief of Lewis.
Lewis then had to be at his best to deny Filipe Teixeira as Albion increased the tempo.
The England Under-21 goalkeeper did well to keep out Teixeira's angled drive by diving to his right.
Peterborough were finding it difficult to take the game to Albion but a cross from Tom Williams on the hour caused a moment's panic in the visiting defence before Carson grabbed the ball.
Seconds later a 20-yard shot from Lee was fumbled by Carson as Peterborough raised their game for the first time in the second half.
Posh, now playing with three in attack, continued their efforts to get back into the game and Boyd almost put McLean through on goal with a clever reverse pass into the penalty area.
In the 69th minute, Lee forced Carson to tip the ball over the crossbar with a deft header but Albion were happy to soak up the pressure.
It was the last real effort from Peterborough who could have fallen further behind had substitute Craig Beattie not been denied by the diving Lewis with three minutes left on the clock.
