Querrey beat Dolgopolov 4-6 6-3 7-5 in the Wimbledon warm-up event while Istomin advanced when Marcos Baghdatis had to retire from their semi-final.
Baghdatis, who was on a nine-match winning run at the tournament, was leading 2-1 with a break in the first set when he pulled up after serving.
He received treatment to his left calf but was unable to continue and will make a decision about whether he plays at Wimbledon after seeing doctors on Saturday.
Baghdatis said: ???I felt my calf pop.
“I was feeling good, I was happy, everything was going my way, and I was a break up early in the match. It’s just the way it is.”
The 2006 Australian Open runner-up and Wimbledon semi-finalist had earlier been drawn to play Donald Young in the first round of the grass court Grand Slam next week.
World No 92 Istomin of Uzbekistan advanced to face Querrey, who got the better of Ukrainian Dolgopolov in a tight encounter.
It looked like a final-set tie-break might be required to separate the duo but Querrey broke in the 11th game, aided by a net cord at a crucial moment, and then served out the match to clinch a spot in the final.