Henman was rarely troubled as he beat Sweden's Jan Apell, ranked No 727 in the world after being out for over a year with a shoulder injury, 6- 3, 6-3 to set up a match with the Slovakian Karol Kucera today.
Henman admitted Rusedski's recent surge up the world rankings is helping him in his own quest to break into the world's top 10.
Henman was British No 1 until August, when Rusedski took over from him. The Canadian-born left-hander then finished runner-up in the US Open before winning in Basle to consolidate his position as No 1 in Britain and move up to world No 4.
Henman's recent victory at the President's Cup in Uzbekistan was unable to lift him higher than world No 21 after he had climbed to a career-high No 14 earlier in the year.
But after beating Apell, Henman insisted: "It's a healthy rivalry. We're pushing each other higher and higher in the rankings and now it's Greg's turn to lead the way."
Henman, who beat Kucera 6-4, 6-1 in Basle last week, added: "Getting Jan wasn't a bad second-round draw and I was happy with the way I played."
The defending champion, Jonathan Stark, reached the quarter-finals of the Heineken Open in Signapore yesterday with a hard-fought second-round win over the Slovakian Jiri Novak.
The 26-year-old American, who upset the world No 2 and top seed, Michael Chang, in the first round, found a timely second wind to prevail 6-3, 3-6, 6-3 in 1hr 27min.
Stark now plays Sweden's Magnus Gustafsson for a place in the last four after Gustafsson, seeded seventh, beat the German Martin Sinner 7-6, 4-6, 6-3 in another tough quarter-final.
The unseeded Stark's win over Novak, who is ranked 22 places above the world No 94, took the American's unbeaten run at the tournament to nine matches. Sweden's Thomas Johansson also advanced to the quarter-finals with a 6-4, 6-4 win over the South African Marcos Ondruska.Reuse content