Hamilton will start fifth following a bizarre coming together with Russell, who lines up in 12th, at the end of Q2 at Barcelona's Circuit de Catalunya.
Pierre Gasly took fourth spot for Alpine, one place ahead of Hamilton, who was half-a-second back, with home favourite Fernando Alonso only ninth in his Aston Martin.
Hamilton had to take on a replacement front wing for Q3 after he made contact with Russell in the closing stages of Q2.
With both Mercedes men starting their hot laps, Hamilton moved out of Russell's tow at 210mph on the main straight.
But the seven-time world champion was forced to take to the grass after his team-mate, who was making his way past Sainz's Ferrari, unintentionally, closed the door on him.
Hamilton kicked up dirt from the grass as part of his front wing flew off his Mercedes.
"George just backed off," said Hamilton over the radio. "That is really dangerous. I might have some damage on the car."
Although Hamilton's time was good enough to progress to Q3, Russell was eliminated in 12th.
"You didn't tell me there was a car behind," said Russell. "I don't know what the hell was going on in this session. The car was bouncing. I couldn't get my tyres working.
Russell will start one place behind Perez after the Red Bull driver also failed to make it out of Q2.
Perez is Verstappen's closest challenger in the championship but a week on from his horror show in Monaco where he finished 16th and two laps down, he qualified only 11th here.
The Mexican ran through the gravel and, although he managed to keep his Red Bull out of the wall, his next lap was not quick enough to carry him through to Q3.
"Unbelievable," said Perez.
On an afternoon of shock results, Charles Leclerc, who started this race from pole position last year, will line last but one on the grid.
Leclerc complained about the rear of his Ferrari and finished above only Williams rookie Logan Sargeant in the order.
"I don't have the answers for now," said Leclerc following his early bath. "The only thing I can say is the left-hand corners were undriveable."
Q1 was suspended by nine minutes following multiple spins on a track drying out after earlier rain.
Alex Albon, Nyck de Vries, Yuki Tsunoda and Valtteri Bottas all ran off the road, and with gravel on the asphalt, race director Niels Wittich red-flagged the session.