Idiopathic pulmonary fibrosis (IPF) is a chronic and restrictive disease characterized by fibrosis and inflammatory changes in lung tissue producing a reduction in diffusion capacity and leading to exertional chronic arterial hypoxemia and dyspnea. Furthermore, clinically, supplemental oxygen (SupplO2) has been prescribed to IPF patients to improve symptoms. However, the evidence about the benefits or disadvantages of oxygen supplementation is not conclusive. In addition, the impact of SupplO2 on the autonomic nervous system (ANS) regulation in respiratory diseases needs to be evaluated. In this study the interactions between cardiovascular and respiratory systems in IPF patients, during ambient air (AA) and SupplO2 breathing, are compared to those from a matched healthy group. Interactions were estimated by time series of successive beat-to-beat intervals (BBI), respiratory amplitude (RESP) at BBI onset, arterial systolic (SYS) and diastolic (DIA) blood pressures. The paper explores the Granger causality (GC) between systems in the frequency domain by the extended partial directed coherence (ePDC), considering instantaneous effects. Also, traditional linear and nonlinear markers as power in low (LF) and high frequency (HF) bands, symbolic dynamic indices as well as arterial baroreflex, were calculated. The results showed that for IPF during AA phase: 1) mean BBI and power of BBI-HF band, as well as mean respiratory frequency were significantly lower (p < 0.05) and higher (p < 0.001), respectively, indicating a strong sympathetic influence, and 2) the RESP → SYS interaction was characterized by Mayer waves and diminished RESP → BBI, i.e., decreased respiratory sinus arrhythmia. In contrast, during short-term SupplO2 phase: 1) oxygen might produce a negative influence on the systolic blood pressure variability, 2) the arterial baroreflex reduced significantly (p < 0.01) and 3) reduction of RSA reflected by RESP → BBI with simultaneous increase of Traube-Hering waves in RESP → SYS (p < 0.001), reflected increased sympathetic modulation to the vessels. The results gathered in this study may be helpful in the management of the administration of SupplO2.