How to add a scrollbar to an HTML5 table?

Instead of assuming as fixed width columns.

CSS

table.tableSection {
  display: table;
  width: 100%;
}

table.tableSection thead,
table.tableSection tbody {
  width: 100%;
}

table.tableSection thead {
  overflow-y: scroll;
  display: table;
  table-layout: fixed;
  width: calc(100% - 16px); /* assuming scrollbar width as 16px */
}

table.tableSection tbody {
  overflow: auto;
  height: 150px;
  display: block;
}

table.tableSection tr {
  width: 100%;
  text-align: left;
  display: table;
  table-layout: fixed;
}

Working Fiddle

If you have heading to your table columns and you don't want to scroll those headings then this solution could help you:

This solution needs thead and tbody tags inside table element.

table.tableSection {
    display: table;
    width: 100%;
}
table.tableSection thead, table.tableSection tbody {
    float: left;
    width: 100%;
}
table.tableSection tbody {
    overflow: auto;
    height: 150px;
}
table.tableSection tr {
    width: 100%;
    display: table;
    text-align: left;
}
table.tableSection th, table.tableSection td {
    width: 33%;
}

Working fiddle

With comments

Note: If you are sure that the vertical scrollbar is always present, then you can use css3 calc property to make the thead cells align with the tbody cells.

table.tableSection thead {
    padding-right:18px;   /* 18px is approx. value of width of scroll bar */
    width: calc(100% - 18px);
}

You can do the same by detecting presence of scrollbar using javascript and applying the above styles.