It was only Everton's third win in 11 league games this season, a run that leaves them dangerously close to the relegation zone in 15th place.
Baines, who scored the winner from the penalty spot on Sunday, told the club's television channel (evertontv) that the players appreciated Unsworth's efforts.
"He has been top drawer," he said. "I've loved the training sessions he's put on and the way he has conducted himself. His talk before the game was special.
"We would like to have given him more, and achieved better results - but we have got him a win, which he deserved, at the least.
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"We know we have good players, players that are better than the league table and our performances at times have been showing," the 32-year-old added.
"It was nice to get a win. It was dramatic, so it feels great but it is nothing to get too carried away with. It is the type of win we should be getting here."
Everton next visit bottom-placed Crystal Palace on Nov. 18.
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
