Bailly, 25, made his first United appearance since the 1-1 draw with Chelsea on April 30, having sustained a knee ligament injury in July that sidelined the defender for five months.
Illness to Victor Lindelof forced Solskjaer to start Bailly in a back three with Harry Maguire and Luke Shaw and the Ivory Coast centre half was one of the standout performers as United kept a fourth consecutive clean sheet.
"Absolutely fantastic, wasn't he?" Solskjaer said. "Not a bad [selection] conundrum, because Eric's a top player. It was his first game since we played Chelsea last year in April.
"He's such a top, top defender and his block from [Mateo] Kovacic is out of this world defending. He's quick, he's strong brave as a lion and it's great to have him back."