In this report, we demonstrate a simple and cost-effective strategy to prepare polycrystalline rutile TiO2 based gas sensors with tunable n/p type response inversion depending on gas concentration, operating temperature, and applied voltage. The effect of surface modification by Ag and Ni thin film on structural, morphological, and gas sensor characteristics is studied in detail. The sensors show excellent sensing performance in terms of sensitivity (sensor response similar to 25 for 0.1 vol. % H-2 diluted in technical air), selectivity (selectivity factor for 0.1 vol. % H-2 is about similar to 24 against NH3, CH4, and NO2 and similar to 8 for CO in the same concentration range), stability (both long-term and short-term), and reaction times (similar to 0.7 min for 0.1 vol. % H-2). The aforementioned performance is recorded at 300 degrees C with applied voltage of 0.1 V. Excluding the power consumption of sensor heater (typically similar to 5 x 10(-5) watt), this applied voltage 0.1 V can reduce the power consumption to 3 x 10(-10) watt. For the first time, we found a critical point, defined with critical-concentration (C-c), critical-temperature (T-c) and critical-voltagel (V-C), at which the response inverses from one kind to another, something intriguing to novel sensing phenomena that can be exploited to tailor the selectivity of the sensors. A physical-chemical sensing model is presented to understand the aforesaid peculiar occurrence.