PHILADELPHIA—U.S. labor unions are plowing money into the 2016 elections at an unprecedented rate, largely in an effort to help elect Hillary Clinton and give Democrats a majority in the Senate.

According to the most recent campaign-finance filings, unions spent about $108 million on the elections from January 2015 through the end of August, a 38% jump from $78 million during the same period leading up to the 2012 election, and nearly double their 2008 total in the same period. Nearly 85% of their spending this year has supported...