In the current framework, the standard parametrization of our Universe is the so-called Lambda cold dark matter (ΛCDM) model. Recently, a ∼4σ tension with the ΛCDM model was shown to exist via a model-independent parametrization of a Hubble diagram of type Ia supernovae (SNe Ia) from the JLA survey and quasars. Model-independent approaches and independent samples over a wide redshift range are key to testing this tension and any possible systematic errors. Here we present an analysis of a combined Hubble diagram of SNe Ia, quasars, and gamma-ray bursts (GRBs) to check the agreement of the quasar and GRB cosmological parameters at high redshifts (z > 2) and to test the concordance flat ΛCDM model with improved statistical accuracy. We build a Hubble diagram with SNe Ia, quasars, and GRBs, where quasars are standardised through the observed non-linear relation between their ultraviolet and X-ray emission and GRBs through the correlation between the spectral peak energy and the isotropic-equivalent radiated energy (the so-called Amati relation). We fit the data with cosmographic models consisting of a fourth-order logarithmic polynomial and a fifth-order linear polynomial, and compare the results with the expectations from a flat ΛCDM model. We confirm the tension between the best-fit cosmographic parameters and the ΛCDM model at ∼4σ with SNe Ia and quasars, at ∼2σ with SNe Ia and GRBs, and at > 4σ with the whole SNe Ia+quasars+GRB data set. The completely independent high-redshift Hubble diagrams of quasars and GRBs are fully consistent with each other, strongly suggesting that the deviation from the standard model is not due to unknown systematic effects but to new physics.