Different methods are used for extracting phytochemicals from plant produce. Some methods require sophisticated and expensive instruments, while others need multiple steps and specialist equipment, leading to an increase in energy, solvents, cost, and time. Here, the effect of incorporating hydrogen (H2) into solvents (that is water, ethanol, methanol) on the extraction of flavonoids (TFC), phenolics (TPC), anthocyanins (TAC), and antioxidants (DPPH and ABTS), as well as the extraction yield from red beetroot, were evaluated. The biggest extraction yield was with the use of H2-rich methanol (HRM) (24.32%). Incorporating H2 into water, ethanol, and methanol led to a significant increase in TPC by 77.34%, 39.02% and 89.07%, in the TFC by 43.30%, 50.5% and 88.87%, in the TAC by 92.62%, 199.5% and 257.41%. DPPH scavenging activity increased by 6.49%, 7.05% and 12.15%, and ABTS scavenging activity by 3.93%, 9.82% and 15.05%, respectively. The extraction of individual phenolic compounds, using various solvents, were different for each compound investigated, with HPLC analysis showing that the levels of some phenolics increased when H2 was incorporated into the solvents. This method, i.e., addition of H2 gas, is suggested as a relatively cheap and practical method for increasing the extraction of phytochemicals using an eco-friendly method.