Bruno Fernandes converted a penalty after just 101 seconds before Shaw doubled the lead five minutes into the second half away to City, who had their 21-match winning streak snapped and a run of 28 games unbeaten across all competitions.
Solskjaer hailed Shaw – who joined from Southampton in 2014 – following his impressive display as the England international continues to impress at Old Trafford after his rocky start to life in Manchester.
"Absolutely incredible," Solskjaer said of Shaw. "He was a massive doubt until after the warm-up. He needed to do the warm-up to be cleared to play. So Alex [Telles] was ready but Luke's performance [was] top. He's aggressive, he's hard to play one against one. When he goes forward on those on runs he's unstoppable. He's just improved so much and he's improving all the time and delighted for him."