Afterwards Hull scored five with Tranmere's outfield player, Theodore Whitmore, looking hopelessly exposed in his emergency goalkeeping role.
Achterberg was injured after 20 minutes when he dived at the feet of Hull striker Delroy Facey.
After treatment off the pitch he limped out of the action with a thigh injury that manager Brian Little revealed could be long term.
Howarth replaced him and had no chance of stopping Ashbee's booming drive in the 34th minute.
Soon afterwards he took a kick in the head in a clash with Stuart Elliott and continued after a long delay - his head wrapped in a bandage.
But he did not reappear for the second half and Whitmore took over after volunteering.
Little said: "I've never known two goalkeepers to be injured before and it was the most bizarre half time I've ever had.
"John was in the treatment room, Russell was about to go to hospital, Danny Harrison was being stitched and Gary Jones was also in the treatment room because of a groin strain.
"Although we had played well up to half time I got the feeling it wasn't going to be our day."
Elliott, who went on to complete a hat-trick to take his tally this season to 19, guided a header beyond Whitmore's reach after 54 minutes.
Tranmere immediately hit back when Eugene Dadi showed great control before shooting past Boaz Myhill.
Tranmere's hopes were soon squashed when Nick Barmby got ahead of his marker to score the third goal in three minutes.
Although Whitmore could not be blamed for the goals, his evident unease and unwillingness to put himself about sapped the confidence from Tranmere.
Hull played at a fast tempo and Elliott lashed in the forth after Danny Allsopp threaded a pass through the defence.
Then Elliott completed his hat-trick with a retaken penalty kick.
Hull completed the rout with Allsopp scoring with a free header as noone challenged.