In this work, we study the X-ray timing and spectral evolution of the transient low mass X-ray binary IGR J17091-3624 during first 66 days of its 2011 outburst. We present results obtained from observations with two instruments, Rossi X-ray Timing Explorer (RXTE)/Proportional Counter Array (PCA) and SWIFT/X-ray telescope (XRT), between 09 February, 2011 and 15 April, 2011. Using quasi-periodic oscillation classifications, power density spectrum characteristics, time-lag behavior and energy spectral properties, we determine source states and their transitions at different times of the outburst. During the first part of the evolution, the source followed trends usually observed from transient black hole X-ray binaries (BHXBs). Interestingly, a gradual transition is observed in IGR J17091-3624 from the low-variability SIMS, commonly seen in BHXBs, to a high-variability state with regular, repetitive and structured pulsations, seen only from GRS 1915+105 (also known as 'rho' class variability/'heartbeat' oscillations). We study the time evolution of characteristic time-scale, quality factor and rms amplitude of heartbeat oscillations in IGR J17091-3624. We also present a detailed comparison of the timing and spectral properties of heartbeat oscillations and their evolution in IGR J17091-3624 and GRS 1915+105.