Multi-format and linewidth-tolerant carrier phase estimation (CPE) is a vital part of digital signal processing (DSP) units for future elastic optical transmissions to relax the laser linewidth limitation. In this paper, an innovative CPE scheme outperforming existing CPEs in both universality and performance is presented and verified for multiple quadrature amplitude modulation (QAM) formats. Based on the technique of extended QPSK partitioning and quasi-linear approximation, accurate phase estimation is determined by calculating the intersection of two symmetric straight lines with very low complexity. Comprehensive simulation results of square 4/16/32/64-QAM not only demonstrate that the scheme can be applied to different modulation formats with a universal structure, i.e., indicate its flexibility in the format-adaptive elastic optical networks (EONs), but also show that the linewidth tolerance is greatly enhanced even in comparison with traditional BPS schemes. In addition, taking 64-QAM as an example, the computational efforts can be significantly reduced by a factor of 15.7 (or 10.3) in the form of multipliers (or adders). The slightly better OSNR performance is experimentally validated in polarization multiplexing 16GBaud 4/16-QAM systems respectively, which shows the potential application for flexible receiver-side DSP unit in EONs.