Morris and Brown combined for 13 rebounds and Steve Nash supplied 14 points to go with five assists as Phoenix logged its fifth win in six games.
Sebastian Telfair chipped in 14 points and seven assists for the victors.
Phoenix put the game away with a 26-12 run over a 7-minute span in the second quarter.
Kevin Love notched a double-double of 25 points and 13 rebounds, but it wasn't sufficient to prevent the Timberwolves' sixth straight loss.
J.J. Barea helped out with 16 points and five assists for Minnesota.