The Magpies climbed out of the bottom three as a result of their win - their first in a Saturday 3pm kick-off since February last year - although £12million signing Shelvey could yet find himself in hot water with the Football Association after an off-the-ball clash with Enner Valencia.
Newcastle raced into a 2-0 lead with just 15 minutes gone and Shelvey played a part in both goals, feeding the ball into Georginio Wijnaldum to set up Ayoze Perez and then picking out Daryl Janmaat with a raking cross-field ball and watching as the full-back crossed for Wijnaldum to score.
McClaren said: "You always worry, the first game. Will he blend in? Will he fit into the team, the balance? It was a perfect balance.
"That first pass forward created the first goal and that cross-field just gives you, because of the speed of it, that extra two seconds that the defence can't recover.
"That's the difference between top-quality midfield players and average ones. He's got the potential to be top. There's a long way to go, but it's a nice start."
The only blot on Shelvey's copybook was his 38th-minute collision with Valencia in which he appeared to body-check the striker, although he was not punished at the time.
McClaren, however, dismissed the incident and was adamant there should be no repercussions.
He said: "I have seen it. It was more handbags. Come on - we're a contact sport. It was shoulder to shoulder and he (Valencia) couldn't move Jonjo Shelvey.
"I have watched it. Let's just talk about the game, not stupid little incidents that might make headlines. The headlines should be about the game, should be about the three points and should be about the win, more positive than that."
Half-time substitute Nikica Jelavic pulled a goal back for the visitors within four minutes of his arrival to spark a concerted fightback by his side, but, although Rob Elliot had to pull of a fine late save from Cheikhou Kouyate, there was no way back.
NEWCASTLE UTD 2 WEST HAM UTD 1
21. Rob Elliot
22. Daryl Janmaat
18. Chancel Mbemba
2. Fabricio Coloccini
3. Paul Dummett 57'
4. Jack Colback
12. Jonjo Shelvey
7. Moussa Sissoko
5. Georginio Wijnaldum
17. Ayoze Perez 80'
45. Aleksandar Mitrovic 90+5'
Subs
11. Yoan Gouffran 80'
15. Jamaal Lascelles 90+5'
16. Rolando Aarons
23. Henri Saivet 57'
26. Karl Darlow
29. Emmanuel Riviere
36. Ivan Toney
Barclays Prem
1 Leicester 44
2 Man City 43
3 Arsenal 43
4 Tottenham 39
5 West Ham 35
6 Man Utd 34
7 Stoke 32
8 C Palace 31
9 Liverpool 31
10 So'ton 30
11 Everton 29
12 Watford 29
13 W Brom 27
14 Chelsea 25
15 B'mouth 24
16 Norwich 23
17 Newcastle 21
18 Swansea 19
19 S'land 18
20 A Villa 12