We aimed to study the complexity and time asymmetry of short-term heart rate variability (HRV) as an index of complex neurocardiac control in response to stress using symbolic dynamics and time irreversibility methods. ECG was recorded at rest and during and after two stressors (Stroop, arithmetic test) in 70 healthy students. Symbolic dynamics parameters (NUPI, NCI, 0V%, 1V%, 2LV%, 2UV%), and time irreversibility indices (P%, G%, E) were evaluated. Additionally, HRV magnitude was quantified by linear parameters: spectral powers in low (LF) and high frequency (HF) bands. Our results showed a reduction of HRV complexity in stress (lower NUPI with both stressors, lower NCI with Stroop). Pattern classification analysis revealed significantly higher 0V% and lower 2LV% with both stressors, indicating a shift in sympathovagal balance, and significantly higher 1V% and lower 2UV% with Stroop. An unexpected result was found in time irreversibility: significantly lower G% and E with both stressors, P% index significantly declined only with arithmetic test. Linear HRV analysis confirmed vagal withdrawal (lower HF) with both stressors; LF significantly increased with Stroop and decreased with arithmetic test. Correlation analysis revealed no significant associations between symbolic dynamics and time irreversibility. Concluding, symbolic dynamics and time irreversibility could provide independent information related to alterations of neurocardiac control integrity in stress-related disease.