The top-seeded Sharapova raced to 4-1 lead and had set points in the 11th game but No. 2-seeded Ivanovic fought back to take the hour-long set in a tiebreaker.
Sharapova earned early service breaks in the next two sets and held for victory, giving her the chance to overhaul
The 17-time Grand Slam champion came into the 2015 season with 996 wins and has had three more on the way to Sunday's final, where he'll meet third-seeded
"It's a goal for the season, so I still have time to get to a thousand," Federer said, smiling. "I mean, it's a really big number, no doubt about it. Love to get it tomorrow, especially in the finals in an ATP event where most of my wins have come.
"If not tomorrow, I hope it happens at the Australian Open. It would definitely be an incredible milestone to reach."
Her sister, Serena Williams, was aiming for a third Hopman Cup title when she partnered
The fourth-seeded Ferrer broke the third-seeded Berdych in the first game, and raced to 4-1.
Berdych hadn't dropped his serve in 34 service games through the semifinals, but surrendered four of eight service break opportunities to the Spaniard.
In the second set, Ferrer received the advantage when Berdych double-faulted on a second break point he faced in the 11th game. The Spaniard improved his record to 8-5 against Berdych, whose finals record slumped to 10-15.
Stan Wawrinka will defend his Chennai Open title in the final against Slovenian qualifier Aljaz Bedene.
Wawrinka, also preparing for his defense of the Australian Open title, beat fourth-seeded David Goffin of Belgium 7-5, 6-3, while Bedene accounted for a third seed this week when he knocked out third-seeded Roberto Bautista Agut of Spain 3-6, 6-3, 7-6 (8) in the semifinals.