A milestone was reached by Steven Gerrard on a night when his team maintained what looks like a straightforward course towards the Champions League knockout stages. But far more important for Liverpool’s ambitions this season was the millstone removed from around the neck of Robbie Keane, whose long-awaited first goal for the club can only add to the feel-good factor that is building around Anfield.

A £20.3 million projected price tag has at times looked a burden for Keane since his arrival from Tottenham Hotspur this summer, but, at the eleventh time of asking, he opened his goal account with the second of a rewarding evening that started with an early strike by Dirk Kuyt and ended, from Liverpool’s point view of at least, with Gerrard’s 100th goal in 448 appearances for the club, a thumping free kick. There was still time for Danny Koevermans to score a barely merited consolation for PSV Eindhoven, but even a rare goal in the debit column was unlikely to dampen Rafael Benítez’s spirits as his team maintained their unbeaten record in all competitions this season.

This was about as straightforward as it gets in the Champions League and, with two wins from their first two games in group D, Liverpool will feel that they and Atlético Madrid, whom they face next in back-to-back matches, are well on course for the last 16. Huub Stevens, the PSV coach, admitted as much afterwards, suggesting that his team and Marseilles were now battling for third place, but Benítez sounded a note of caution, recalling how his own team recovered from a calamitous start last season to reach the knockout stages at the expense of Marseilles, whom they trailed by six points after three matches.

That was a characteristic attempt by Benítez to keep heads out of the clouds and he followed it with more of the same for Keane, for whom praise of his first goal for Liverpool came with a typical caveat from his manager. “Before, people were talking about this, so it was important for him and for us,” Benítez said. “But maybe now we will talk about his first goal in the Premier League. Because he’s a striker and he’s ambitious, I’m sure he will be looking now for his first goal in the Premier League and a lot of them in the future.”

For the record, Keane’s wait for a goal ended in the 34th minute of this game. This equated to the 686th minute of competitive action for his new club, a shade under 11½ hours. But the Ireland forward will be relieved that it did not drag into a second day, as was the case with Peter Crouch three seasons ago. As such, the sense of relief that greeted Keane’s goal was not quite as overwhelming as when Crouch broke his duck here against Wigan Athletic in December 2005, but it was palpable nonetheless.

Keane’s goal was the highlight of another rewarding night for Liverpool, but, on the pitch at least, there are positives just about everywhere that Benitez might care to look. Keane and Fernando Torres are beginning to combine well in attack, Albert Riera is showing up well on the left wing, the defence looks very solid — or at least it did until Martin Skrtel lost track of Koevermans after 78 minutes — and, best of all, Gerrard, with a little help from Xabi Alonso, is running into the form where he bestrides the pitch like a colossus from his favoured position at the heart of midfield.

Mark Hughes, the Manchester City manager, would have been forgiven the odd grimace as he and Eddie Niedzwiecki, his first-team coach, took the opportunity to check on the team they take on at the City of Manchester Stadium on Sunday. They were still settling into their seats in the directors’ box when Kuyt gave Liverpool the lead in the fourth minute, beating Andreas Isaksson with a powerful low shot after the former City goalkeeper had kept out a Torres volley from Gerrard’s corner. PSV’s defending was abject, but nobody in a red shirt, least of all Kuyt, was complaining about that.

With Keane adding the second, a cunning side-foot finish past Isaksson after an excellent run and cross from Torres down the right, it seemed only to be a question of how many Liverpool would score, but thereafter they seemed prepared to conserve their energy for the weekend. The exception was Torres, but he, his assist for Keane apart, would endure a frustrating evening, requiring treatment after a couple of sly kicks from Carlos Salcido and then uncharacteristically missing the target when set up by an awful back-pass from Jan Kromkamp.

Rarely can a former player have returned to Liverpool as unnoticed as Kromkamp, which was probably an apt reflection of an Anfield career that amounted to 18 matches in 2006, but he did play a part in PSV’s consolation, cutting inside to cross to Koevermans. By that stage, Gerrard had made things safe for Liverpool, completing his century of goals in spectacular style and celebrating in a jubilant manner that should destroy the myth that such milestones mean nothing to footballers. Moments later he took his leave to a standing ovation.

Keane had already departed to similar acclaim by that stage, with Ian Rush, sitting in the directors’ box, among those who rose to their feet to applaud him. Neither Keane nor anyone else at Anfield these days will get close to Rush’s record of 346 goals for Liverpool, but at least now he has got the most difficult one out of the way.

Liverpool (4-4-2): J M Reina — Á Arbeloa, M Skrtel, J Carragher, F Aurélio — D Kuyt, X Alonso, S Gerrard (sub: R Babel, 82min), A Riera (sub: Y Benayoun, 68) — F Torres, R Keane (sub: Lucas Leiva, 76). Substitutes not used: D Cavalieri, D Agger, A Dossena, J Mascherano.

PSV Eindhoven (5-3-1-1): A Isaksson — J Kromkamp, D Marcellis, T Simons, C Salcido, J Bréchet (sub: E Pieters, 46) — E Méndez (sub: B Dzsudzsák, 76), S Wuytens (sub: D Koevermans, 60), J Culina — O Bakkal — N Amrabat. Substitutes not used: Cássio Ramos, F Rodríguez, M Zonneveld, S Nijland. Booked: Marcellis.

Referee: F Brych (Germany).