After trailing by six points at halftime, the Rockets came out re-energized and refreshed in the third, outscoring the Kings by 12 in the period.
However, sloppy play reigned supreme down the stretch, as the Rockets mustered just 20 points in the fourth quarter while allowing the Kings to drop 30 (their most in any one period) in the game's final frame.
DeMarcus Cousins played arguably his best two-way game of the season in the win, scoring 17 points and grabbing 16 rebounds while taking a big charge and scoring clutch buckets in the game's final minutes.
The Kings shot 49 percent from the field and 32 percent from three while the Rockets struggled to find their stroke from beyond the arc, hitting on 25 percent of their attempts from distance on a night when they shot 48 percent from the floor.
James Harden, Shooting Guard
The first Rockets scorer into double figures, James Harden capped off 2013 by leading Houston in scoring, dropping a season-high 38 points (including 16 in the third quarter) on 12-of-26 shooting (5-of-11 from three) on Tuesday night. Harden also grabbed 10 rebounds in the loss.
However, as has often been the case, Harden opted to save most of his energy for the offensive end.
And if you want to know just how weak Harden's defensive effort was early on, all you have to do is check out Marcus Thornton and Ben McLemore's numbers.
In his first 12 minutes of action, Thornton scored 15 points on 6-of-8 shooting, while McLemore added 13 points as he capitalized on easy looks from start to finish.
To Harden's credit, he did ramp up the defensive intensity a bit in the second half, but when it comes to tight games like this one, the Rockets could have used a full 48 minutes of defense from The Bearded One.
"New Years wish -- we understand a possession in the 1st half is just as important as the 2nd half," Rockets general manager Daryl Morey tweeted after the game.
They also would have appreciated fewer turnovers from Harden, who committed a team-high five on the night, including back-to-back giveaways on key possessions down the stretch.
Were it not been for a sensational and perhaps game-saving second half, Harden's grade would have been lower.
Dwight Howard, Center
After posting a doughnut in the first quarter, Dwight Howard went to work on the inferior trio of Quincy Acy, Jason Thompson and Aaron Gray, scoring nine points in less than four minutes to start the second period.
In total, Howard finished with 13 points in the quarter and 15 on the night while pulling down eight rebounds in a key one-on-one battle with Cousins. He blocked only one shot and went 5-of-11 from the free-throw line in the loss.
It's safe to say that Howard was thoroughly shown up by Cousins, who not only posted a double-double, but also ripped four steals in the win.
Howard was fortunate that Cousins saw just nine first-half minutes after picking up two early fouls, too, because his production tapered off considerably in the second half as the Kings big man bodied him up in the post.
Chandler Parsons, Small Forward
It was a steady but relatively quiet night on the scoring front for Chandler Parsons, who scored 13 points on 5-of-11 shooting (1-of-7 from three) and committed three turnovers.
And just like Harden, Parsons was only capable of making an impact on one end of the floor, as Rudy Gay dropped 25 points, including 17 in the first half on 6-of-9 shooting.
It was hardly Parsons' worst outing of the season, but the Rockets could have used some better defense and his usually reliable three-point stroke on Tuesday evening.
Jeremy Lin, Point Guard
Jeremy Lin was arguably the Rockets' steadiest player from start to finish on New Year's Eve.
Not only did Lin lead the team with six assists, but he helped contain Kings point guard Isaiah Thomas to 6-of-17 shooting.
Needless to say, Lin's defense on several big-name point guards has been stronger than expected in Patrick Beverley's absence.
Lin added 14 points of his own while racking up two steals and a block in a tidy and complete performance.
Terrence Jones, Power Forward
During a first quarter in which the Rockets scored 24 points and committed five turnovers, Terrence Jones was the team's lone bright spot.
Jones attempted to set the tone over the game's first 12 minutes with his energetic play on both ends of the floor, racking up four points, three rebounds, a steal and a block in that time frame.
This statement pretty much summed up the performance of Kevin McHale's squad, with the exception of Jones, during the quarter:
Maintaining his hot play at Toyota Center, Jones finished the night with 12 points, 11 rebounds and four blocks. He was one of five Rockets players to finish in double figures.
Aaron Brooks, Sixth Man
With Lin the preferred option at the point on both ends of the floor, Aaron Brooks saw just 15 minutes in relief of the Rockets' starting floor general.
Brooks provided a nominal performance against the Kings, managing four points and three assists while shooting 1-of-5 from the field and 0-of-3 from beyond the arc.
He's certainly had better nights.
It was another quiet evening for Houston's shorthanded bench.
Aside from Brooks, Omri Casspi and Francisco Garcia were the only contributors of note off the pine for the Rockets, logging 15 and 16 minutes, respectively.
Casspi led the duo with six points on 2-of-7 shooting and five rebounds, while Garcia added four points. They also helped contribute to a 9-0 Rockets run toward the end of the third quarter.
Until Beverley, Omer Asik and Greg Smith return, McHale will continue to rely heavily upon the production of his starting five.
The Rockets will have two days off before they host the New York Knicks at 8 p.m. ET on Friday night.