Victory for Cilic will give his team an unassailable 3-1 lead in the best of five series and a place in November’s final against France who wrapped up their semi-final against Spain on Saturday afternoon.
Zeljko Krajan, the Croatia captain, told the television channel HRT: "Cilic is a big favourite. It will definitely not be easy to defeat him in front of a home crowd."
The United States fashioned themselves a lifeline on Saturday when Mike Bryan and Ryan Harrison won a dramatic doubles match.
The American duo raced into a two set lead but Ivan Dodig and Mate Pavic won the next two to force a decider. That went to a tiebreak. Bryan and Harrison clinched it seven points to five to end nearly five hours of battle.
If Johnson manages to overcome Cilic for the first time in their seven meetings, the semi-final will be decided by one of the rising stars on the circuit.
Borna Coric, 21, the world number 18, will play 20-year-old Frances Tiafoe. The American, ranked 40th, will go into the clash as the underdog.