Hamilton, Bottas's team mate, started in eighth place after a grid penalty triggered by an unscheduled gearbox change and finished fourth.
England's star batsman Kevin Pietersen clashed with his skipper Alastair Cook on the eve of the fifth Ashes Test in Sydney.
Formula One's post-season shake-up took another spin on Tuesday with Williams announcing the departure of technical head Pat Symonds while Valtteri Bottas moved closer to Mercedes and Felipe Massa's retirement looked to be coming to an end.
After England collapsed from 288 for five to 302 all out, New Zealand initially struggled in reply before Williamson and Taylor took the game away from the hosts with a clinical 206-run third-wicket stand.
The Ferrari driver is one point ahead of Williams's Juan Pablo Montoya and two clear of McLaren's Kimi Raikkonen with two races remaining after Monza.\n\n
England held their nerve to end Australia's last-wicket partnership of 65 and seal a dramatic 14-run victory in an extraordinary first Ashes Test at TrentBridge on Sunday.
The Australian third seed was too strong and too consistent for the 15th-seeded Slovak as he won in 94 minutes.
Lewis Hamilton can clinch his fifth Formula One world championship at Sunday's US Grand Prix.
England have named uncapped Surrey batsman Jason Roy in their 14-man squad for next Sunday's one-off Twenty20 international at home to India.
The 23-year-old Finn has 48 points compared to the 44 of Ferrari's second-placed Michael Schumacher.
Championship leader Kimi Raikkonen gave McLaren their third straight win on Sunday.
World champions Michael Schumacher finished sixth.
England made a poor start to their Australia tour on Thursday with their fancied bowling attack forced to toil by a second-string Western Australia Chairman's XI at Perth.
Reigning F1 champ warns Bottas about Hamilton rivalry
The Finn was running third when he was forced out of the Malaysian Grand Prix with transmission failure on lap 40.
Formula One world championship leader Sebastian Vettel won the Bahrain Grand Prix for Ferrari on Sunday in the German's 200th race start.
A summary of Friday's night's qualifying matches for Euro 2020.
The Colombian had a blistering late lap to outpace his German team mate at Williams Ralf Schumacher.
Kimi Raikkonen says his McLaren needs to be more powerful as well as more reliable if he is to win the championship this season.
'I'm quite satisfied, especially because Raikkonen was only third and picked up just one point as a result not a lot happened,' said the German world champion.
Ralf Schumacher won the French GP as his team celebrated their second one-two finish in the space of a week.
Centurion Steve Smith praised Australia's bowlers after they reduced England to 107 for eight in the first innings to set up a victory bid in the fifth and final Ashes Test on Friday.
The seventh seeded Thai lost to Spaniard Feliciano Lopez in the first round.
Stokes took three quick wickets late in the afternoon session to quash a brief Australian fightback and two more victims late in the day helped England restrict the touring side to 241 for seven at the close, still 90 runs behind the hosts.
Teenaged opening batsman Haseeb Hameed was one of the three uncapped players named on Friday for England's forthcoming tour to Bangladesh.
Nico Rosberg won the Austrian Formula One Grand Prix in a Mercedes one-two finish on Sunday to stretch his championship lead over team mate Lewis Hamilton to 29 points after eight races.
The McLaren driver took the fight to Michael Schumacher with the top time in the first qualifying for Sunday's European GP.
Three-time world champion Lewis Hamilton dominated practice at the season-opening Australian Grand Prix on Friday, putting Mercedes on top of the timesheets and leaving his Formula One rivals with plenty to ponder before the weekend.
Lotus driver Kimi Raikkonen is in no rush to make a decision over his team for 2014 despite speculation linking him to a move to champions Red Bull with Mark Webber stepping away from Formula One at the end of the season. Raikkonen, who is third in the standings, is out of contract after this season having been one of the most impressive drivers since returning to F1 last year.
Australia will be desperately hoping to play a full game under clear skies when they face arch-rivals England in their must-win Champions Trophy clash in Birmingham on Saturday.
Ferrari's world champion is looking to extend his 896-day run at the top.