The heavy reliance of real-time precise point positioning (RTPPP) on external satellite clock products may lead to discontinuity or even failure in time-critical applications. We present an alternative approach of real-time undifferenced precise positioning (RUP) that, by combining satellite clock estimation and precise point positioning based on the extended Kalman filter, is independent of external satellite clock corrections. The approach is evaluated in simulated real time with the assistance of a variable number of IGS multi-GNSS stations located between 1359.7 and 4852.5 km from the users. The results show that even with a single auxiliary IGS station, RUP is still feasible and able to retain centimeter-level positioning accuracy. Typically, with three auxiliary IGS stations about 2000–3000 km away, an accuracy of about 2 cm in the horizontal and 5 cm in the vertical can be achieved. The performance of RUP is comparable to that of PPP using 5-s satellite clock products and notably exhibits superior short-term precision in dealing with high-rate (1 Hz) GPS/GLONASS observations. The addition of GLONASS observations reduces the convergence time by 56.9% and improves the 3-D position accuracy by 31.8% while increasing the processing latency by a factor of about 1.6. Employing three IGS stations over 2400 km away from the epicenter, RUP is applied for the rapid determination of coseismic displacements and waveforms for the 2016 Kaikoura earthquake, yielding highly consistent results compared to those obtained from post-processed PPP in the global reference frame. We also explore its potential in facilitating real-time online services in terms of real-time precise positioning, zenith tropospheric delay retrieving, and satellite clock estimation.