The Blues bounced back from suffering their first league loss of the season against Larne by beating Loughgall 2-0 at Lakeview Park on Saturday.
While Crusaders also did the same, following up a derby defeat to Cliftonville last Monday with a routine triumph over Glenavon at the weekend.
That victory means Linfield go into tonight’s crunch clash with their fellow title-challengers sitting at the summit one point clear of second-placed Larne - who travel to Loughgall – plus have a two-point gap on Crusaders.
The Crues haven’t picked up a victory at Windsor Park since Billy Joe Burns and Gavin Whyte netted in a 2-1 win back in December 2017 while Healy’s men are undefeated at home in their last 17 league matches.
However, Baxter will lean on the fact that Crusaders went unbeaten across their four Premiership meetings with the Blues last season, which included two home victories alongside two 0-0 stalemates on the road, and former Northern Ireland international Healy says it’ll be another testing encounter for his side
"Crusaders are in around the top and have started the season very well, albeit they'll have been disappointed by the result against Cliftonville last Monday night,” he said. “It'll be a tough game and we always have a tough encounter with Stephen and his boys.
"We'll be expecting more of the same on Tuesday."
A topic of discussion that has dominated local football over the past week is the possibility of summer football being introduced in Northern Ireland.
NIFL CEO Gerard Lawlor outlined their ambition to implement a change to the Irish League playing calendar in the organisation’s new five-year strategy which was unveiled at Windsor Park on Wednesday.
"As a manager, I don't get paid enough or am not qualified enough - I will let the club discuss it,” added Healy. “We want the league to thrive.
"But as I say, there are people who get paid a lot more than me and are a lot more qualified to make those decisions."