Begovic insists he would not swap the partnership between Shawcross and Robert Huth for any other central defensive pairing in the country.
The pair helped the Potters achieve their eighth clean sheet of the campaign in Saturday's goalless draw at Aston Villa.
Begovic said: "We take great pride in our defensive record and our defensive work and it's working well so far.
"I wouldn't swap our two centre-backs for anyone else in the country and I don't just say that because I play with them.
"They look so solid as a partnership with a great understanding. It works wonders.
"Ryan made his England debut last month (as a substitute against Sweden) and I think he has the class to become an England regular eventually if he keeps going the way he is.
"He is still very young, has played a lot of Premier League games and is our captain.
"We really rate him and the more times he is with the England squad, the more times he plays, the more comfortable he will feel and he will show his true colours."
Stoke stretched their unbeaten run to six games via the share of the spoils at Villa and have collected 14 points during that period.
Begovic said: "It was important to keep our run going. Villa away is always a tough game and we had to grind a result out.
"We weren't at our best, unlike the last few games, but we kept the run going.
"Villa came out really hard at us with a lot of pace and energy, which we knew they would as a young team and we withstood that.
"We could have been a bit better going forward but we are really pleased with our squad.
"We've had a few injuries here and there which have unsettled the team but we've got good quality to come in anywhere.
"It is a sign of a club progressing which is really important."