Danny Graham and Sone Aluko scored in the first half before substitute George Boyd netted after the break.
Dawson received a guard of honour prior to taking his seat on the bench but it was not long before the 34-year-old was back on his feet to celebrate the first goal.
A Robbie Brady free-kick landed on the head of Graham, who nodded in his first Hull goal from eight yards out.
The Tigers doubled their lead just after the half-hour mark, when Aluko curled in a wonderful left-footed shot.
Tempers frayed after Nono's challenge on David Meyler and the visitors' robust approach continued in the second half, when Markus Steinhofer received a caution for a foul on Maynor Figueroa.
Hull made six changes on 73 minutes and one of the substitutes netted the third goal five minutes later, when Boyd latched on to a poor backpass before rounding the keeper and finishing from close range.
Dawson's final appearance in a Hull shirt came two minutes from time, when the Scunthorpe left-back was introduced from the bench to take the acclaim of the 7,991 crowd.