A desirable flooding-based time synchronization protocol inWireless Sensor Networks (WSNs) should neither demand fast propagation of up-to-date time information nor keeping track of the neighboring nodes. Moreover, such a protocol is strictly required to have low computational and communication overhead as well as small memory footprint. Would there be a protocol which meets these requirements' We answer this question positively by introducing a novel time synchronization protocol whose main component is "adaptive-value tracking". Thanks to this component, each sensor node synchronizes the rate of its clock to that of a reference clock through successive feedbacks with a considerably low computational and memory overhead. By adjusting time offset of the rate-synchronized clocks, the network-wide synchronization is established even without demanding rapid propagation of the reference clock and keeping track of the neighboring nodes. In the light of our experimental evaluation in a testbed of 20 MICAz sensor nodes, we observed that the proposed protocol provides similar synchronization under the same communication frequency with an approximately 97% less CPU overhead and 80% less memory allocation compared to the recent flooding based time synchronization protocols in WSNs.