Many wireless sensor network applications require real-time communication, and real-time applications require packets to reach destination on time. However, applications may send packets with different priorities and hence delay bounds for packets may vary significantly. Therefore packet differentiation in the network is essential for meeting the deadline requirements. We propose a routing protocol that supports real-time communication by utilizing transmit power adjustment in order to meet the deadline of urgent packets and use energy efficiently. Our protocol also provides packet scheduling and gives precedence to urgent packets. We have conducted experiments on our sensor network testbed to observe the effects of transmit power on end-to-end delay. As expected, increasing transmit power increases the range and link quality, and reduces the number of hops to reach destination. Therefore adjusting transmit power has a great effect on delivery time and can reduce the end-to-end delay. Our protocol, Real-time Routing with Priority Scheduling and Power Adjustment, uses different levels of transmit power for packets with different priorities. It sends urgent packets with maximum power to minimize end-to-end delay and lower priority packets with reduced power to save energy and balance the load on nodes. Simulation results show that our routing protocol increases the deadline meet ratio of packets and reduces the transmit energy spent per packet when compared to routing protocols that use fixed transmit power. Additionally, results indicate that our approach lessens the interference on sensor nodes that are caused by other transmissions and helps balancing the load on the nodes.