Heading into the match Querrey led their head to head 3-1, but the Cypriot won their last meeting on the hardcourts in Sweden at the Stockholm Open in 2015 7-6(2), 6-1.
Querrey makes a quick start
It was the fifth seed who came flying out of the blocks, racing into a 3-0 lead after the Cypriot handed the American a break following a double fault.
Querrey looked strong on serve throughout, holding with relative ease as the American broke the 31-year-old for a second time before closing out the set 6-1 on serve with a forehand down the line winner.
Far more competitive second set
After a series of service holds Baghdatis gained his first window of opportunity at 0-30 on Querrey's serve in the sixth game after striking a backhand down the line winner. The American responded with some big serving to get to game point and despite the Cypriot pushing the fifth seed to deuce he had no joy as Querrey held serve.
The ninth seed managed to push the American to 30-30 in his following service game but still could not find a way past the fifth seed as he continued to bomb down first serves to hold for 4-4.
Querrey, who was yet to drop serve in the tournament, faced further pressure at deuce in the tenth game. The American managed to hang on once more, outlasting his opponent in an extended rally as he held serve.
A tight and tense tiebreak
In the second set tiebreak, Baghdatis netted two backhands to hand two mini-break to Querrey as the American went to the change of ends with a 4-2 lead. The 31-year-old hit two consecutive aces to pull it back to 5-4 before gaining the mini break back to make it 5-5. The fifth seed held his nerve by putting away a volley to get to match point, but the ninth seed denied the American after hitting an ace down the middle.
Querrey saved a set point with a cross-court backhand winner before he was denied on his second match point by the stubborn Cypriot. Baghdatis was rewarded for his efforts as he sealed the second set tiebreak 10-8.
Baghdatis maintains his momentum in the decider
The fifth seed appeared to be suffering from a lull after the disappointment of the loss of the second set as he dropped serve for the first time in the tournament in the opening game of the final set. Baghdatis was able to consolidate the break after being pushed to 30-30 and deuce as he held to take a 2-0 lead.
The 31-year-old was under severe pressure on serve in the sixth game down two break points but came up with some important first serves to hang on to the crucial break. The fifth was not to be denied a second time as the American ripped a cross-court backhand winner to pass the Cypriot and level the score at 4-4.
Baghdatis responded superbly, capitalising on a Querrey double-fault and backhand unforced error to break the fifth seed, finishing with a backhand crosscourt passing shot winner. The Cypriot then closed out the match on serve to book a quarterfinal match up with second seed Pablo Cuevas.