The 48-year-old youth team coach stepped up to take on reserve-team duties and help out with the first-team when Paul Dickov's backroom staff were placed on gardening leave on New Year's Eve before taking the reins on a temporary basis when the Scot resigned a fortnight ago.
Philliskirk led Latics to their first League One win in 10 attempts against MK Dons last weekend before overseeing Saturday's dramatic 2-2 draw with Everton in the fifth round of the FA Cup - hours after watching his youth team play out a 1-1 draw with Rochdale.
"I think he is the busiest man in football and I've got a lot of time for Tony, he's a top man," Baxter said.
"He's done a fantastic job, he doesn't half do a lot of homework on the opposition and it works.
"He works us really hard in training, he tells us what's good to do and what's not good to do against the opposition.
"It showed against MK Dons, we were fantastic.
"I didn't really think we'd get a better manager than Paul Dickov but I think Tony Philliskirk is doing a great job."
Oldham can move out of the League One relegation zone with victory over Stevenage on Tuesday night, and the magnitude of that game left Baxter and co with no time to bask in their impressive performance against his former club.
He added: "It was home for me to rest up, no celebrations. We've got a massive game on Tuesday night against Stevenage and, for me, it's a bigger game than the Everton one was."