His first goal came in the 35th minute. Stuart Green's corner went to Damien Delaney who was totally unmarked. He should have buried the header but goalkeeper Ben Foster blocked it. However, Allsopp was able to bundle the rebound in from a yard out.
Goal number two was scored in the 58th minute. Green made a good run down the right to put in a cross to the back post. Stuart Elliott nodded it down well, and Allsopp volleyed it low into the net. It took a slight deflection off a defender, but Foster had no chance.
City really should have had the game wrapped up after completely dominating it, but the introduction of Hector Sam gave Wrexham a chance. The lively forward pulled a goal back in the 75th minute from the edge of the box after City failed to clear.
Five minutes later, the visitors came close to what would have been a shock equaliser. Boaz Myhill made a great save from Chris Armstrong's shot, and the ball pinged about the area with Leon Cort also having to stop it on the line before it was finally cleared.
Wrexham again came unbelievably close to stealing a point two minutes into stoppage time as Darren Ferguson's superb long-range shot went just wide.
It would have been a severe punishment for the Tigers if they had conceded an equaliser after having so many chances to put the game to bed, but they got the three points they deserved even though it was by just the odd goal.
City line-up (4-4-2): Myhill; Stockdale, Cort, Delaney, Dawson; Price, Green, Ashbee, Elliott; Allsopp, Barmby.
Un-used subs: Duke, Edge, Lewis, Hessenthaler, Facey.