In this work we study the critical behavior of the absorbing state phase transition exhibited by the contact process in a linear chain with power-law diluted long-range connections. Each pair of sites is connected with a probability P ( r ) that decays with the distance between the sites r as 1 / r α . The model allows for a continuous tuning between a standard one- dimensional chain with only nearest neighbor couplings ( α → ∞ ) to a fully connected network ( α = 0). We develop a finite-size scaling analysis to obtain the critical point and a set of dynamical and stationary critical exponents for distinct values of the decay exponent α > 2 corresponding to finite average bond lengths and low average site connectivity. Data for the order parameter collapse over a universal curve when plotted after a proper rescaling of parameters. We show further that the critical exponents depend on α in the regime of diverging bond-length fluctuations ( α < 3).