R: ifelse loop across multiple dataframes

I'd like to create an efficient ifelse statement such that if columns from df2 match columns from df1, then that row in df2 is coded a specific way. My code works but is very inefficient.

Example data:

Df1

A        B      C
111     2     1
111     5     2
111     7     3
112     2     4
112     8     5
113     2     6

Df2

A        B
112     2
111     2
113     2
111     5
111     7
112     8

Desired Outcome:

Df2

A       B       C
112     2     4
111     2     1
113     2     6
111     5     2
111     7     3
112     8     5

What I've done is this:
Df2$C<- ifelse(Df2$A == 111 & Df2$B == 2, 1, 0)
Df2$C<- ifelse(Df2$A == 111 & Df2$B == 5, 2, 0)
Df2$C<- ifelse(Df2$A == 111 & Df2$B == 7, 3, 0)...

This works, but is there a way such that df2 could reference the columns in df1 and create column df2$C, so that each combination doesn't have to be manually typed out?