So, because everyone is posting their solution and none was good for me, here is mine (tested on Chrome & Firefox).
table { height: 1px; } /* Will be ignored, don't worry. */
tr { height: 100%; }
td { height: 100%; }
td > div { height: 100%; }
Fiddle: https://jsfiddle.net/nh6g5fzv/
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Edit: one thing you might want to note, if you want to apply a padding to the div in the td, you must add box-sizing: border-box;
because of height: 100%
.