The Swede finally notched a PGA Tour win after 188 starts, finishing at 20-under 260 on the TPC River Highlands in Connecticut.
The pair were knotted at 20-under entering the final hole when Moore nearly holed a bunker shot for birdie, rolling it 4 feet past the cup. But his par try was short, and Moore ended up with a costly bogey, falling one stroke behind.
Jacobson then made him pay by tapping in the short par putt for the win.
Michael Thompson carded an 8-under 62 for fourth place at minus-18, while James Driscoll fired a 3-under 67 for sole possession of fifth at minus-16.