To some extent they were helped here by the Kings, who won a penalty just after the hooter but elected to kick the ball out for an attacking lineout rather than limit the damage. They had little to gain from extending the match and the Blues finally found their ruthless side to capitalise.
Li's try, which came via a behind the back flick pass from Guyton, was celebrated by his teammates, who would have gone into the match knowing a bonus point victory was the bare minimum for Umaga.
This was not a complete performance by any stretch. Loose forwards Steven Luatua, Jerome Kaino and Tanerau Latimer were prominent, as was lock Patrick Tuipulotu, but the backs again suffered from a lack of direction and there was a sloppiness to the early exit plays, as if they believed they automatically had the right to run the ball from their own line rather than work for it.
Wing Melani Nanai's two tries from two attacking lineouts in the first half - which followed James Parsons' from a driving maul - put the Blues in charge, but in front of a sparse crowd at the Nelson Mandela Bay Stadium, the Kings weren't about to give up without a fight.
Surprisingly, the Blues' scrum was put under pressure at times and in hooker Edgard Marutlulle and flanker Thembelani Bholi, the Kings had two forwards who impressed with their speed and attacking intent.
Marutlulle's try, combined with a 50m penalty from fullback Jurgen Visser, put the Kings within striking distance at 22-18 with 20 minutes to go before Guyton's two significant interventions.
"We came here with a job to do and, look, it wasn't pretty, it was probably the story of our year, but we're rapt with the win," skipper Parsons said afterwards.
The defeats by the Chiefs and Hurricanes, added to this win by the Blues, means the New Zealand conference has become more condensed and Umaga will feel there is plenty to play for still.
They take on the Lions in Johannesburg next weekend, a team several notches up from the Kings, but they have got a significant monkey off their backs and will probably go in the match at the foreboding Ellis Park with a great deal more confidence as a result.
Blues 34 (Melani Nanai 2, James Parsons, Billy Guyton, Tevita Li tries; West 3 cons, pen)
Kings 18 (James Hall, Edgard Marutlulle tries; Elgar Watts pen, con, Jurgen Visser pen)
Halftime: 19-10
Blues v Kings - Match centre