Bates will have scans on her right knee in coming days after the leg twisted underneath her in a tackle at the Kennedy Community Centre on Saturday.
Umpires held up play for several minutes before Bates was taken off the field on a stretcher, as teammates showed support for their much-loved skipper.
The Hawks also lost Laura Stone (concussion) after an early head clash with an opponent and were 11 points down at halftime.
But they piled on five unanswered goals in the third quarter - four of those before Bates' injury - to set up their 6.5 (41) to 4.6 (30) victory.
It lifted Hawthorn (3-2) into the top eight, leapfrogging the Bulldogs (3-2) on percentage.
Three-time All-Australian Bates reached her 100-game milestone a week earlier, but is now set for a lengthy period on the sidelines.
Webster was proud of his players' response to the injury.
"It's incredibly difficult (to remain focused). I've seen numerous times in AFLW different ways where this has really impacted groups," he said.
"Credit to our players, they kept their minds on the job, as challenging as that was, and were able to dig deep and finish the game off.
"Now we'll get around Batesy once we work out what's going on with it and support her as best we can."
Hawthorn's Irish key forward Aine McDonagh fired in attack with a career-best four majors, extending her lead at the top of this season's goal-kicking list.
McDonagh has kicked 16 majors in five outings this season.
Eliza West (24 disposals), Tamara Smith (20) and Jasmine Fleming (19) also shone for the Hawks, as did ruck Lucy Wales.
Isabelle Pritchard had game-high tallies of 31 disposals and eight clearances for the Bulldogs, with Elisabeth Georgostathis (19 touches) also busy.
The Dogs kicked three of the first four goals but were held scoreless in the third quarter as Hawthorn took control of the contest.
Also on Saturday, Sunny Lappin kicked three goals and sparked the second-half surge that led to Gold Coast's 30-point win over Collingwood.
The Suns (3-2) kicked four goals to one in the third term - two of those to Lappin - to set up their 9.8 (62) to 4.8 (32) victory at People First Stadium.
Maddy Brancatisano kicked two goals, Charlie Rowbottom had 29 disposals and Dekota Baron provided the highlight of the day with a towering mark-of-the-year contender.
Mikayla Nurse suffered a nasty cut on the face after a head clash with Suns teammate Lucy Single late in the match.
Tarni White had 29 disposals for Collingwood (0-5), who remain winless this season.
