The individual sprint starting field has been whittled down from 27 to 12, with the winner in each of the six second-round heats advancing to the quarter-finals later in the day.
"It's one-on-one and Sam's very tactically astute, so we'll be looking for him to push his way through," Elliott said. "But as we've seen, the Brits are in fantastic form, the Russians are in great form, and so are the French. It's going to be tough."
Defending champion Jason Kenny of Britain clocked 9.551 seconds in breaking his own Olympic record while teammate Callum Skinner had the second-fastest time with 9.703sec in qualifying.
Webster, who qualified ninth-fastest, won the latest bout in his ongoing rivalry with teammate and good friend Eddie Dawkins when he won their first-round match sprint.
Dawkins had qualified 10th, just 0.015sec slower, and the pair did battle to decide who would go through.
Webster, 25, who won gold over Dawkins in the individual sprint at the 2014 Glasgow Commonwealth Games, held on to record a 10.159 sec time and another win over the 27-year-old Southlander.
Dawkins was forced to ride in the repechage where he was edged out by Germany's Maximilian Levy.
The pair had combined with Ethan Mitchell the day before to win silver behind Britain in the team sprint.
Earlier, Natasha Hansen and Liv Podmore didn't get the start they wanted and missed out on progressing through the women's team sprint qualifying.
They posted a disappointing time of 34.346sec, the slowest time in the nine-strong qualifier.
China's Gong Jinjie and Tianshi Zhong went on to beat Russia in the final to win gold with defending champions Germany taking bronze.
- AAP
