Manager Ally McCoist believes Rangers can no longer be seen as the soft touches of the Irn-Bru Third Division.
The Light Blues finally picked up their first away win in the league this season with victory at Clyde.
Rangers were previously held on their travels by Peterhead, Berwick and Annan, and suffered a humiliating defeat at struggling Stirling Albion, as they struggled to adapt to their new surroundings.
However, McCoist feels his side are now showing the aggression and competitive nature required to come out on top in Scottish football's bottom tier.
He said: “You have to match up against the opposition and let them know that you're as much up for the competitive side of the game as they are.
“It's safe to say that every team we'll play this season will certainly be up for the game and will be competitive and aggressive, which is absolutely fair enough.
“We must be equal to that, if not stronger than that.”
He added: “If I'm playing against Rangers in SFL3, one of the first questions I would ask is 'do they fancy it? Let's have a look and see if they're up for the battle'.
“The vast majority of the footballing public might think we do have better players than SFL3 but, that said, you've got to earn the right to play.
“If somebody doesn't want to let you play and is aggressive, you have to combat that. You have to face up to it and match it.
“I do not have a problem at all with the level of competition and aggression that's been shown towards our team.
“The wee problem we probably had is we've not matched up to it
— and we're maybe doing that now.”
Goals from Dean Shiels and Lee McCulluch secured the win at Broadwood and, according to McCoist, hard work also had a big part to play as Rangers moved two points clear at the summit.
He said: “You can talk about the great opening goal — and it was a great goal.
“But the main reason we got the result today was because we worked our socks off.
“The one over-riding factor that should always be there is a desire to work your socks off and they got their rewards because of that.”
Clyde manager Jim Duffy felt the dismissal of John Neill proved to be the turning point in the game, with Rangers leading by a single goal at the time.
Neill was red-carded after 68 minutes after picking up a second booking for clashing with goalscorer Shiels.
The Bully Wee boss said: “It was just a split second loss of control and I really don't know why John was getting involved because it was nothing to do with him. When there's a little melee, it's standard practice now that the referee will book everybody involved.
“It was a silly thing and it put the nail in the coffin as far as us having a chance to get a result.
“From Rangers' point of view, they'll be delighted.
“Most people will think they'll get a head of steam up and should stretch their advantage at the top now.”