Webster won through to the quarterfinals after a day of super fast times for sprinters at Saint Quentin en Yvelines. He was forced through the repechage, ousting team mate Eddie Dawkins in the process, and was to meet Russian Denis Dmitriev in the quarterfinals today.
Earlier, Dawkins was third fastest in the 200m qualifying in 9.681sec, bettering his own national record, and Webster 17th fastest at 9.848sec.
The sprinters took advantage of the sticky conditions and wider turns in the velodrome to produce some stunning times.
Former world champion Stefan Boetticher (Germany) clocked 9.641sec and Gregory Bauge (France) 9.676sec to lead the way. Dawkins was just 0.005sec behind the Frenchman.
The Kiwis progressed through the first round of sprints but both were beaten in the second round, Webster by Australian rival Matthew Glaetzer and Dawkins by Venezuela's Hersony Canelo.
They drew the same repechage, where Webster executed perfectly to win the one spot in the quarterfinals.
Aaron Gate, the 2013 world champion, produced a stunning points race to finish fifth in the six event omnium.
Lying 12th coming into the final race, Gate was outstanding, away in two breaks and eventually gaining three laps on the field to win the points race. Such was his haul, finishing in the points in eight of the 16 sprints, that he catapulted himself into medal reckoning in the closing laps.
He finished with 173 points, only eight points from the podium and his 81 point haul in the points race was a massive 28 clear of the second best.
Fighting back from a broken collarbone, his form in the timed races was well below his best, but he is encouraged by the result.
''It's disappointing not to be on the top of the podium here but I knew I did not have the form in those timed events,'' Gate said.
''To come away in the points race, which is now the crucial event in the omnium, with nearly double the points of the second placed rider, is something I am happy with.''
Previously, each of the omnium disciplines scored a standard number of points, but now the total score in the points race is added to the overall to determine the winner.
Gates clocked 1min 6.297sec in the 1000m time trial and 13.359sec in the flying lap, both well outside his best, before his onslaught in the points race.
Rushlee Buchanan produced a brave effort in the 10km scratch race, pushing clear with a powerful burst 10 laps from home. Working with one other rider, Buchanan put half a lap on the field but the big guns closed down the break three laps from the finish.
Powerful Dutch rider Kirsten Wild controlled the final lap to win the sprint from Australia's Amy Cure. Buchanan finished in the front group in 12th.
On Saturday, Southland sprinter Matt Archibald cemented a break out season with his first world championship medal.
The 28 year old earned bronze in the 1000m time trial, matching his result from last year's Commonwealth Games, and he set the fastest time at sea level by a Kiwi in the process.
It was New Zealand's fourth medal at the world championships, a tally which came agonisingly close to increasing when teenager Regan Gough missed a medal in the 40km points race on a countback.
