Anthony Osmond, 52, of Velindre, Carmarthenshire, admitted unlawfully wounding Gareth Jones after he started dating his daughter Oasis, 20.
Swansea Crown Court heard Mr Jones, 29, needed surgery in September 2015 to repair a cut to his heart.
Osmond fled but was caught by police.
Helen Randall, prosecuting, told the court the couple kept their relationship secret at first because Osmond was "overprotective and obsessed with Oasis".
When they eventually met, Osmond and Mr Jones got into a fight at the Nags Head pub in Pembrokeshire, and Osmond stabbed him with a 15cm-long (6in) kitchen knife.
Osmond made off in his car and police later stopped him as he approached the Second Severn Crossing in Monmouthshire.
During police interviews, Osmond told officers he did not think Mr Jones was "appropriate" for Oasis.
Janet Gedrych, defending, said Osmond had not picked up the knife deliberately and was "devastated at how close he came to killing that young man".
An "overprotective" father who stabbed his stepdaughter's new boyfriend in the chest because he did not approve of him, has been jailed for two-and-a-half years.