The 31-year-old Croatian had a forgettable season last year, sliding down the world rankings from seven to 39, his lowest year-ending position since 2007.
But he has started this season well, rallying from a set down to beat Austria's Dennis Novak in Sydney on Saturday before overcoming Poland's Kacper Zuk 7-6 (10/8), 6-4 on Monday.
It helped Croatia win the tie 2-1 at the inaugural team event to reach a strong position in Group E, which also features Argentina and Austria.
Cilic, whose career high was beating Roger Federer to win the US Open in 2014, is eyeing a deep run at this month's Australian Open.
He made the semi-finals at Melbourne Park in 2010 and lost to Federer in a five-set epic in the 2018 decider.
"I feel motivated. I feel that, you know, 2019 was a season that I could use to learn some new things," said Cilic, whose wife is expecting their first child in February.
"All those things are good motivation for me to get stronger and now to push a little bit further into 2020.
"I had good time off in the off-season, trained well," he added, after pulling out of the Davis Cup in November with a knee injury.
"I believe this event can definitely set things up nicely for the rest of the season."
A veteran of Australian conditions, having played the Australian Open since 2007, he said he was as prepared as possible for what could be wild weather changes at the Grand Slam in Melbourne.
"Melbourne is very tricky with the conditions. It can go from 40 degrees day to 20-degrees day. And even on a couple of occasions, two years ago, during the day was 40 degrees, and then you get into the night when it's already 18, 17," he said.
"So you've got to be ready for everything. For those extreme conditions, nobody is basically prepared."
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