The pair featured in midfield for the 3-0 friendly win at Wembley.
And Arsenal midfielder Rice, captain for the night, said of Anderson: "He has taken it all in his stride and is playing like he plays for his club. When you have a lad who is that confident and comes in and feels he does not have to do anything different, it's like auto pilot the way he plays.
"We have built up a really good relationship in midfield, we have had close relationships there, and we are playing closer together."
He added, "We are building up a nice little partnership. The manager has really liked us in the last three games, and we just have to keep building on that.
"The World Cup is in the summer and there is still a long way to go. The more we can play together and keep building momentum will be really important."