A brace from striker Miller boosted the Somerset side's Sky Bet Championship survival hopes and earned the hosts their first back-to-back wins at Huish Park this season.
The on-loan Nottingham Forest striker impressed throughout alongside former Hearts midfielder Palazuelos - and the duo's performances left Johnson purring as Yeovil extended their unbeaten run to five games.
Johnson said: "It was a super win. We showed a lot of commitment and effort, and Sheffield Wednesday came into the game on a rich vein of form. It's nice to go five matches unbeaten with another home game against Ipswich coming up on Tuesday.
"It's very tight down the bottom with other teams all getting results, but we're in there and we could even drag a couple more teams down there with us. There are now probably six or seven teams in the mire down the bottom of the league.
"Ishmael [Miller] has a booming shot on both feet - the first goal was a right-footed volley and the second was a bit of class, coming inside and bending it in the top corner with his left.
"They were two worthy goals and he deserved his man of the match, but Ruben Palazuelos had a great debut. It's one of the best debuts I've seen. He was quiet, clever and competitive.
"If we stay up, it's because we've got a striker who scores every other game, and that's really important. We needed to find a striker with that ratio and now we have, and that's also brought all the other lads up to the fore."
After seeing his side's impressive nine-match unbeaten run away from Hillsborough come to an end, Sheffield Wednesday head coach Stuart Gray criticised his side's "under-par" display.
Gray said: "I thought we bossed the game in the first ten minutes without really threatening the goalkeeper. We had good possession and got into some good areas, but then whether we thought it was going to be easy or whatever, Yeovil showed the fighting spirit that you do when you're in the bottom three.
"They thoroughly deserved the win in the end, we didn't win enough one-against-one battles but I'm just disappointed with an under-par performance. We've had nine games away from home on an unbeaten run, but that wasn't us today.
"I'm disappointed in the manner we conceded the first goal, and the second goal is a 'worldie'. Suddenly we were chasing the game but we couldn't get a foothold - our passing was really poor.
"We had a fantastic following but they've got a long journey home and we haven't given them anything to celebrate."