Belisarius' answer works well if you are willing to work with indexes. If you prefer to work with the elements themselves, here is a rule-based solution.

    innrJoin[data : {{_} ..}, a_, b_] := 
      data /. {x___, y : PatternSequence[{a}, ___, {b}], z___} :> {x, Flatten[{y}], z}

    innrJoin[{{1}, {2}, {3}, {4}}, 2, 3]
>{{1}, {2, 3}, {4}}

    innrJoin[{{a}, {b}, {c}, {d}}, a, c]
>{{a, b, c}, {d}}

Edit -- new and improved algorithm :-)